Deep litter method plus worm composting?

Though I've had chickens for many years now, I've never felt like I'm adequately addressing the issue of poo. I'm planning to make major changes in this department though, so I'm here for advice. I use the deep litter method, very poorly, but also planning to improve on that front. I'm going to get better about removing poo and adding bedding. That's another question for another thread. What I've done to address the existing poo in the coop is to bring our old worm composting bin from when we tried keeping worms to the backyard and put it by the chicken coop. It was totally empty. It's a wooden crate, elevated off the ground on posts, with three inner compartments (two removable wire baskets and one open area). Today I mucked out the chicken coop and added new straw. I put the old nasty wet crap stack into the worm composter to "cook" hopefully.

My question is, can I and should I try to add worms to this? I'm not planning on composting anything else in there. I'm afraid that even though the crap/straw has been in the coop all winter, it might still be too hot and it will kill the worms. I'm also not sure if there's any benefit to adding worms. If they don't die, will they help it compost faster? Also, at one point I had tried a sand/gravel floor, so plenty of that also got into the bin when I was shoveling. Will that be bad for the worms?

Side note: what are your favorite coop cleaning tools? I feel like a complete dummy when I'm shoveling out the coop. It's so physically difficult and my method feels so ineffective!