Hi, welcome to BYC!
I would think since the moisture is a problem in the winter and you will need to make adjustments for that already, why not just leave it in place for summer? I don't mind the smell of fresh laundry, but it can be a bit much at times. We use a half dryer sheet for this reason. And it's my understanding that chickens have more sensitive respiratory system than humans. Also, you can go stand out there and see if it seems to strong for you or not. And you could always go with unscented detergent, though I prefer some smell. But I have to use softener to stop static electricity. SO I have gone to dryer sheets since I don't want the other stuff going into my septic and therefor my land... I guess I don't know if they make unscented dryer sheets.
Also, lint traps will need to be cleaned often and depending on the size of holes the chickens may find a way to eat it anyways. It's surprising how much they put out. Back in the day washing machines had a lint trap to...
Seeing your set up, I might just consider moving the coop a little farther away. Instead of doing any reconstructing or trying to spend on those expandable bendy tubes to extend it. Those will likely develop holes from wear and tear from the chickens doing daily activities and they have a greater chance of building debris on the inside and possible causing a fire. Solid tube pipes like a chimney vent style on would be more durable, less likely to build lint on the wrinkles, but also pricier.... Oh, but now I remember you have sand in that run not just the grass. That could be harder to move than I was originally thinking.
Chicken keeping has been a very dynamic and learning experience for me. So many things I thought would work really didn't. Other things I thought wouldn't, have... Good thing this is great helpful community with lots of people to share their experiences. And what works for one may not work for another. And that is OK, Just try to figure out what works best for you.
5 feet might be enough. We get pretty strong winds and there is often a breeze. You say they free range when you are home... maybe do laundry then. Also, when it raining it's about 100% humidity anyways (slight exaggeration) in the coop. It stays 75% in my house even with the heater running. Our low is 60 ish %. So I would expect it to be higher than indoors out there. Evaporation under my covered but not enclosed patio happens pretty good, so the dryer really shouldn't add too much to the humidity load.
What else is surprising... is the lengths some of us will go through to accommodate our beloved pets!