adult foster dog having accidents in crate

I am currently fostering a dog from my local shelter and he is perfect in every way aside from not being housebroken, which we are struggling with. Finding him a home will be soooo much easier if he is potty trained so I am looking for advice!

He is about 2 years old and was neglected in his previous home – emaciated, and kept in a basement. I've had him for a little over 3 weeks and I have been taking him for frequent walks on a regular schedule and rewarding with treats every time he pees or poos – he is super food motivated, goes to the bathroom every time I take him out for a walk, which is down to 4-5 times per day, and now excitedly turns for a treat after he goes. Overall he's doing great outside, and never has an accident when we are home and watching him. However, I have been crating him when I leave the house (because I can't trust him to not have an accident while I'm gone) and he is consistently going in the crate. I have also tried leaving him out of the crate but in my bedroom with the door closed for short periods of time when I need to give my cats a break from him, and he will also have accidents when left alone in the room, even after just coming in from a walk. I cannot figure out how to break the habit of him going in the crate because I'm not there to correct it when it happens. And for context, when he gets crated I walk him immediately before putting him in there and am gone no longer than 3 hours (often less), which I know he is capable of holding it for – he holds it through the night every night for up to 8 hours. He does seem to have a bit of separation anxiety, but the shelter veterinarian declined anxiety meds and he settles in the crate shortly after going in, and there is really no way around the crate at this time bc I need to keep him separated from my cats when he is not supervised and I can't have him peeing and pooping all over my house. Any tips would be greatly appreciated!!