I use bagged compost in my run, and throw in greenhouse cuttings fairly often. Works great! (P.S., my run is covered with tarps, so is fairly waterproof. What with waterer spillage, and what leaks around the edges of the tarps, it is usually pretty dry. During the summer, I wet it down with a hose every day).
We've been talking about using tarps atop the run. I built the walls of the run to be over 6 feet high, and will be adding a "roof" for shade and protection for aerial predators. We stationed this run on the east side of the house, which gets the least amount of rain, but I'm still worried about the first rain fall. The run is about 1/2 complete with many more hours of work ahead of us, as I just had to design a modular version that could be disassembled and reassembled elsewhere on our property. (I'm starting to think I'm a bit of a masochist.

)
We have a shed filled with stuff we haven't looked at for about 10 years that I'm trying to convince my husband into letting me convert into a larger, secure and protected chicken coop for my more mature birds...once I actually have mature birds. I think I'm wearing him down, but until I see things going to donation or the dumpster I won't know for sure.
I'm also thinking of raising black soldier flies this spring. I really do prefer to feed my birds wholesome, natural foods more indicative of what chickens evolved to eat. (I'm a food snob at heart, I guess.)