my coop is enclosed and off the ground. I have covered the plywood floor with peel and stick laminate sheets for easier periodic clean outs (and think I’ll have to drill a few holes in bottom for drainage)
If you use dry deep bedding, then you don't need to drill any kind of drainage holes. The coop bedding should absorb all the chicken poo.
Will wood chips still work as a composting base in there? If not, what do you recommend for traction for their little feet that won’t need to be cleaned daily? I have access to free wood chips and I have an abundance of pine needles.
Since your coop is enclosed and off the ground, you are probably going to have a dry deep bedding system. A composting system (deep litter system) inside the coop needs to have lots of moisture to keep the litter at the consistency of a wrung-out sponge. I don't think you want that in your setup. To start your litter to compost inside the coop, you would have to add water and turn over the litter to encourage active composting.
I don't want to add any moisture to my dry deep bedding litter here in northern Minnesota because it would just freeze solid in our winters. Also, in your case, your peel and stick laminate sheets would probably start to lift off in no time if they get wet.
Wood chips and pine needles work great for bedding. If you can get them for free, then it's a great option. I used wood chips as dry deep bedding for my first two winters. It worked great. The last two winters I switched over to using paper shreds which I make at home with my office paper shredders. Free bedding is almost the best option in my book.
The advantage that paper shreds have over wood chips is that when you clean out the coop, the paper shreds will compost much faster than wood chips in the compost bin or your chicken run composting system. Also, when it is time to clean out the coop, paper shreds are much lighter to haul out.
It often works well to add more bedding on top as needed, and then clean it all out at intervals (maybe twice a year, maybe more or less than that.)
Because I live in northern Minnesota with long winters, I typically clean out my coop twice a year. In the late fall, before the snow falls, I clean out my coop and put down a fresh layer of paper shreds (or wood chips) of about 2 inches. Then, I add more fresh paper shreds on top of the old litter about twice a month. Just enough to keep everything looking good. I do this all winter long and by springtime, I might have as much as 10 inches of paper shreds in the coop. But my coop was designed to hold up to 12 inches of litter. If you don't have that much room for deep bedding, then you have to periodically take out some litter before you put in fresh bedding.
Chicken poo freezes hard as concrete in my winters. I don't clean out my coop until after the spring thaw. Then all the old litter/bedding gets tossed into the chicken run composting system. Twice a year cleaning is more than adequate to keep my coop looking good and not smelling bad. If you ever start to smell that chicken urine smell, then you need to either add more litter on top of the old, or clean out the coop. I have found that adding a thin layer of fresh bedding on top of the old bedding, about every two weeks, all winter long, keeps me ahead of any bad smells.
Where I live, in the freezing cold winters, there is basically no smell to frozen poo. So, I just add fresh paper shreds on top of the old. In the springtime, the poo thaws out and if I have enough paper shreds as bedding, the poo and urine usually gets absorbed into the shreds. Almost all the chicken poo is directly under the roosting bar, so if I ever have to take out any litter due to a smell, it will be under the roosting bar. But fortunately, I have been able to stay ahead of that situation with periodically adding more fresh bedding on top the of the old bedding.
Then chickens naturally freshen up the deep bedding with their normal scratching and pecking. If any area needs more attention, I'll toss some chicken scratch on that area and let the chickens go to work. When the chickens scratch and peck for food, any chicken poo will automagically disappear into the lower layers of the bedding. That is almost a perfect self-cleaning system. Twice a year coop clean out is all I need, and to be honest, I think I could go maybe once a year. But, converting coop bedding to compost for the garden is one the main reasons I have chickens, so I want to add that coop litter to my chicken run composting system at least twice a year.