I'm thinking in our area, your original 4 x 4 coop with 4 x 10 run is a bit small for 12 birds, could work for 8 birds. But the new shed idea is too large for 12 birds, mainly because of the head space. If your birds, like mine, can be out most of the time in a run or the yard...you'll be feeling the itch for a few more birds over the summer.
I moved the roosts down to about 8 inches off the floor. I use the deep litter method, our secretary at work gives me all the shredded paper I can use! I just keep adding to it about every two weeks. Since they have decided to nest in the rear corner of the side nearest in the photo, they walk through all the poop to get to the nest, resulting in dirty eggs. So each morning I sprinkle a bit of new bedding over the poopy places.
Hubby also found a piece of 90 degree bent aluminum flashing (about 8" wide, bent in half, sharp edges though so he rolled them on some sort of machine...got 12' cheap at Home Depot), cut it to 8' and put it over the ridge so that rain and snow can't get in. But we didn't seal it too tight so that moisture can still escape.
Things I would have done differently...place the gangplank ramp farther to the far end. It is currently almost centered with the food being on the far end. That whole half of the coop is just linoleum, no bedding so the bedding doesn't go down the ramp. I bought my pullets at 20 weeks and they had been kept on gravel in a dog run, no roosts or other places to sleep. So mine don't roost much, they tend to hunker themselves down...on the linoleum...in their poop. I have two that do roost over the bedding area. And none of them will use any kind of nesting box, they lay their eggs in a neat little nest they stomp out in the corner of the bedding...thus, they all walk across the poop with poopy feet from sleeping in it, to lay an egg. So if I would have moved the pop hole farther down, I could have put the bedding and barrier to hold it farther down, more bedding to walk across (think wiping their feet) before getting to the nest. It would have also forced them to sleep in the bedding instead of on the minimal amount of bare linoleum.
Food and water inside really doesn't take up as much space as I thought it would, about one foot square each. And I keep my food and water inside because of the wind we get some days. (they get greens and scratch in the run each morning).
But because they cannot keep this A-frame coop warm during the winter I'm building a new, smaller coop for them. It's two stories, but it does not cover the run. The footprint is 2 x 4 x 4H, with two stories inside and the food being fed in thru a tube...storage and filling of tubes from the outside. So essentially their floor space will be 4 x 4. It doesn't sound like enough space for 6 birds. But my neighbor has this set up with 6 barred rocks and they have plenty enough space for the night.
Because it is so dry here, and our clear nights get cold so fast, I would be tempted to get more birds if you use the shed for a coop. Mine is 2 x 8 and they can't keep it warm, I want to put at least 4 more large birds in there. With yours 10 x 6 you should evaluate space once you get your birds in there and then plan on more! Otherwise I think you may need auxilary heat in the winter.
Since my coop is so small, relatively speaking, I heat a large granite rock on the hearth during really cold weather (can also heat in the oven at 250 for a few hours!) and put the rock near where they tend to sleep in the coop. That helps on single digit nights to keep the coop around 25 degrees, plenty warm for my RIR's. But 10 x 6 and I'm guessing it's also 6 feet tall. That's a lot of air space for the birds to keep warm at night.
Of course all of this is predicated on the fact that my birds have the 4 x 8 run to play in while I'm gone during the day (and they don't seem to feel crowded in there), and they get out to free range during nice weather (no snow on the ground) several days each week.
If you use the shed I would consider:
-more birds or heat in the winter
-place things strategically so that poop is not in the path of the feeders or the nests, and you don't have to walk through poop to fill feeders
-put nest boxes (all 6 of mine use the same dug out nest even though I gave them 3 real box nests to start with) and roosts in as soon as you can so the birds start to use them right off
-figure out how you are going to open the doors to the run, especially when there's snow on the ground
-keep the run covered...winter from snow, summer from the sun
Most of all, have fun with your birds!