We don't really have good space for a garden since we live in the woods but after doing a little research I am going to try plants that are shade tolerant (lettuces, broccoli, cauliflower, etc.) With that research in hand I can't wait to use my coop and run contents for the garden this spring. I used to use pine shavings for the coop and leaves in the run but switched over to mulched up leaves for the coop this fall. I was tired of raking & mowing to just burn everything so this year I mulched up enough leaves and put them under a tarp for coop and run use. The run in the summer time breaks down pretty quick. I am hoping the nitrogen does not burn up my plants but I am going to give it a try with what I have been saving over the winter. I will rototill a few coop cleanings into the soil as soon as the thaw has happened here in Michigan.
Since your coop and run contents are going to be already (mostly?) composted, the fresh poop in what you pull out for the garden should not be too hot to burn plants.
Of course everyone has their own approach with soil management, but we've stumbled upon methods that are not very common, so I thought I'd share. We've adopted a 100% no-till system. We had poor yields last year, but we had macronutrient deficiencies. We'll continue the no-till regimen this season with some proper amending and hope to have a great year (ask me in the fall how well it went).
All that to say it's POSSIBLE to forego tillage and cultivation as weed control if a person wants to. Others have had great success with them. You can just lay compost, organic matter, mulch on the surface of the ground and the micro and macro organisms will "till" them in for you. They are far more efficient than a rototiller. For instance earthworm secretions actually "cement" their tunnels open; talk about the perfect way to get water infiltration into the root zone! Fungal networks can be vast and they are excellent at transmitting nutrients. Both things (and some many other things) are quite fragile and are easily destroyed by tillage. There are many advantages of no-till, not the least of which is it eliminates a major chore and the equipment/energy required to do that chore.
It takes time to get a system like that up and running, especially if your soil is low in organic matter to start with. Some people start with an initial tilling in order to incorporate sufficient organic matter, then transition to no till.
Once you have a healthy no-till soil, all you do is use mulch and mulch a LOT. The mulching will slow soil warming in the spring. I know a farmer that got around this by just pulling the mulch back in the spring as seeds germinated or transplants took hold. Once they are established, then back the mulch goes.
Leaves make EXCELLENT mulch. Leaves (and rotting wood) are the main way forests stay fertile and thrive. Definitely save all you can!
BTW many clovers are quite shade tolerant, and make an excellent, nitrogen-fixing, weed suppressing companion plantings. Grow 'em between your veggies, especially heavy feeders like those brassicas you mentioned, and they'll help attract pollinators, too!
Good luck and have fun!
