I'm really sorry to hear about this
@cluckmecoop7.

I know what's it like to get overwhelmed and frustrated by the birds. Especially when you have this one hen, that no matter how hard you try, just won't shut up and be happy, but will complain about everything, even in her sleep. Or even that random hen that is ALWAYS escaping no matter what you do, and that's including clipping EVERY flight feather off her wings, and she STILL gets out...
Here's what I do, even though my birds are like pets/babies/children/friends/emotional support animals/anything else that they could be to me:
Depending... I rehome my "retired" birds at 2-3 years old. I like to go the Craigslist route (here's an article that I wrote about posting on there:
https://www.backyardchickens.com/articles/how-to-post-on-craigslist.76257/, and any other questions that you may have, I'll be more than willing to answer, and just plain helping you out with Craigslist. Might even be willing to help you post them to find a good home if you want.

) With the "Retirement Plan" I don't get too much of an overstock of birds, though breeding them always put the numbers up fast. True, I've cried over rehoming my retired birds before, but I'd rather have them go to a good home, than be overwhelmed and stressed out by them.
Also, vacation. Vacation is a MUST. Especially the more birds you get. I take anywhere from a week to a month long vacation from my birds. This is simply a camping trip, but if you can't go camping, just set up the flocks and don't go near them for a time. Many a time, have I got overwhelmed by the flock's (raising 50-100 Cornish Xes can really put me over the edge), and a good vacation straightened me out. Taking care of birds can be a big responsibility, and a little time to get away, breathe, and let the stress go, really helps.
With the retirement, and vacation, those are what helps me out. As far as them being "pets" my birds are pets that lay eggs. Once retired, they find new homes with owners who will either let them free range on their big farm, or keep them as pets themselves. A couple of my hardest birds to rehome went to a home where they was going to be spoiled out of their minds. Often have I found that the home that they were going to, was better than the home that I was already giving them.
As far as not having the time for them.... Chickens actually don't need to have a lot of time spent with them. Unlike cats and dogs, they'll be fine without your attention. (Just you'll probably see a change on friendliness.) All you need to do is basically feed, water, collect their eggs, and open and close their door, with the occasional health check. (If you're as in tune with your birds as I am, you'll know something wrong before they even show a symptom.)
Chickens can be easy to take care of, especially your average birds. Now, as voice of experience, bantams CAN be a different situation. My bantams was the best things that I had. They were perfect in every way. They listened so well. They did exactly as I wanted, with no mess ups. Perfect. Until somebody else "tried" to take care of them. They'd be high up in trees and on the house and everything, just not where they was supposed to be. When I was away, I'd get the most complaints about them, than any other flock I had. And on top of things, the rooster, Chester, would chase and attack everybody as part of his nature. I loved and adored my bantams, but they can be a handful to some people. And with ANY bird, in "training" they can be fusterating, but once they learn something, it sticks with them. (If it's an escaping thing, clip one wing of primary flight feathers and if they're going under something, block the escape with wood, or use tent stakes to hold fencing down.)
Now on ducks... Chickens are easier! Why? Why are chickens easier? How? Water. Ducks need water 24-7 that is deep enough for their head to dunk in. Their beak should be able to completely fit under water to keep their nostrils clean. (That was told to me by an expert.) If you're concerned about winter, ducks are harder do to needing this water. It freezes on them, and if you have a pool, frostbite on feet can happen. Ducks also can be messier. Unlike chickens, they don't scratch around their bedding, so it gets messy fast. Also, on top of all that, the extra water during warmer month, equals more MOSQUITOES! Doesn't always depend on whether or not the water is redone everyday, there's still that extra water that mosquitoes can breed in. Ducks do love mosquito larvae, but when the water drainage is outside their run, there's nothing that they can do.
On winter, what is it that you're not ready/prepared for? My coops are usually year around coops. (My bantams were an exception..) Only thing I'd sometimes be needing is waterers. I always down size the waterers, and go from a hanging 3.5 gallon waterer to a 1 gallon waterer base waterer. (A rubber waterer is also highly recommended by many, though I don't do that due to birds wanting to stand in the water.) (Having more than one 1 gallon waterer for one flock is good to have to switch out when one is frozen or broken.) I like to estimate how much water they'll drink before the waterer freezes, and give them only, or a little over that. I go out several times a day to check on the waterer to make certain my birds have water, and the waterer is breaking from ice. I don't leave waterers out overnight, due to the water freezing before they'll drink it during the night.
As far as coop cleaning during the winter, I do deep litter compost. True, that comes with it's own set of issues, but for me, it's the easiest thing to do. I don't clean the coops out at all during the winter, just add shavings as needed. Majority of my birds have been cooped up all winter, with the deep litter compost. It supposedly keeps the birds warm, and you get a couple months break of cleaning out the coops. Basically, you switch coop cleaning for waterer checking. If it's the bantams and frostbite that you're worried about, everybody says VENTILATION. With my bantams, I would put a cage in their coop, cover with something like a blanket for insulation, and do the deep litter there. That worked well for them, though they could beg to differ. (They wanted lots of space, but lots of space was too cold.) It kept them warm on the cold nights.
On feed costs going up, more than you're looking to spend, growing birds will keep eating more and more till full grown. I suggest down sizeing. Or, depending, try going a different brand of feed. Don't buy
TSC feed, because it's not trust worthy, so I've heard, but buy from a local non chain feed store. Poulin Grain is, I think, $15 a bag, though the kind my flock actually needs, so therefore uses, is $20 a 50 pound bag. And that sure beats the $30-35 for the same size bag of grain that used to be gotten for the birds. Cheaper grain isn't always the best, but it's affordable, and puts grain (and not bread) in their crops.
1. Should I sell my chickens?
Maybe not all, but rehome the retireds. Don't sell. Retired birds won't sell. Even if they're pets. Just because they're free, doesn't mean that they can't get a good new home. Or, if you can't bring yourself to rehome your retireds, rehome the "Birds of Trouble." Basically the birds that are being the most pain in the neck. The birds that make you want to drive your head through a wall and scream while pulling your hair out till you're bald. Your Birds of Trouble will overwhelm and frustrate you way too quickly and should just go to someone who doesn't notice that a bird squawks too much, does the EXACT opposite of what you're telling them to do, or anything like that.
2. Should I just cut back on numbers?
I think that'll probably help. A great way on deciding who, is either do the Retired of 2-3 years and older. Or, if you can't do those, rehome the Birds of Trouble. (Often Birds of Trouble ARE newbies, but that's because they don't know nothing, and haven't learned anything yet. Young pullets are often my Birds of Trouble until they learn what I want of them.)
3. Should I completely drop chicken keeping and do ducks or something?
No, I don't think so. Ducks are nice, and the Swedish Hybrids of Moosehead Lake, Maine was my joy during the time that I had no chickens last year do to, actually in one way, a similar situation as you, plus traveling a lot. But, they just wasn't the same as chickens. I held them and even had one spend the night in my bed one night, but they wasn't chickens. Ducks need different things and stuff than chickens, and I see them as more work, especially without a pond or something. And maybe chickens are just dear to me because of personal issues.... But I see chickens as the better option.
4. How could I sell what I call "pets"?
I've done it. I've cried over my birds. For months I was so mad at myself thinking "How could I let 'Ginger' leave?" I watched Ginger do everything that she possibly could do trying to get back to me. She didn't want to leave at all. She was desperate to stay with me. But I letted her go. I knew that she was going to a good home, and Bella had really pushed me over the edge, so I couldn't do it anymore. And even with my bantams, I'm still regretting rehoming them. Even the person who got them could tell I didn't want to let them go. Even though she had drove a long way to get them, she asked me if I really wanted to let them go. I wanted to keep them, but I knew she'd give them a good home, and being gone all the time, it wasn't good for my bantams to be cooped up all the time, so I let them go. Out of all my birds, Ginger and the bantams was the hardest, but now I've seen good reasons for them to have all gone, and me to restart all over. Starting with the issue that I was dealing for years, and couldn't get a hold of it. Restarting fixed that issue, along with a few others. It can hurt, but rehoming your chickens IS possible.
Ok, so I THINK that's covered everything. I'm sure I forgot a bunch of stuff to say.... Also, sorry if the post is too long...
~Lacy Duckwing