CoH will collect if you take it down (not contractor) and get it within 10ft of the curb. I think limits are 30" diameter, but the debris crew that came by my house last week said "any size, we'll haul it away".
Not sure where you are. We have a tree guy we've used 3 times now and neighbor has used as well. He's always offered us great pricing, on time, works fast. He's not insured though, FYI. But if the tree is already down and he's just cutting and hauling, doesn't seem as risky.
When my tractor gets out of the shop I'd be happy to come help you move it to the street if my tractor will fit in your backyard. Don't know when it will get back though, that's the only problem.