It's always good to read about dogs with issues getting into the right home. You are most certainly doing things right.
So this is a 3rd home and a lot of continual changes. The goal is to make experiences positive. I suggest one thing at a time, building on what you are already doing. I wouldn't wait for a noise to be over to cheerfully say "good noise" so he knows it's the bark/car/other loud noises that you like, not their stopping.
- Start SLOW, break it down. First is the collar/halter issues. It helps if you have a harness that needs minimal fussing with-- over his head, legs in, snap shut. If you have someone to help, pick him up and do it so he can't fight much. If not, don't bother with treats... use praise and a very matter-of-fact tone. I would spend 3 or 4 days putting it on him, "GOOD BOY".. take it off. Do it every hour or 2. He'll eventually get bored of the energy expenditure and accept the reality.
2, Since being outside is important for you, and it's good for him, that might be a good place to start teaching him that you are the giver of good stuff.
At what point does he stress about outside? Once you are out the door, or going to it?
If he's anticipating and stresses once you put a leash on him, put a leash on and walk around the house. Sit in different rooms, pet, up talk, after no more than 10 mins, treat and let go.
Do this until he's comfortable, then have a chair near the door and make that your final stop.
Once comfortable with that, open the door and look out with him. Next step is sitting a chair outside. Then sitting the chair in the grass outside. Treats and praise. Next walk him to the road, come back, sit in the chair, pet and praise, go in and remove the harness. Slowly extend the distance.
Note on nails... Dremels are great, but I'd start with one toe at a time. If you do one every few hours, you can get one paw done the first day; 2nd day do 2 nails each time. By the 3rd day the nails will be done. Soon you'll be able to do all of them at once. Or not. Sadly there are some dogs for whom doing nails is a fight to the death. If all else fails, just pay the vet's office to do them, or cut holes in a pillow case like they do cats, drop him in it and hold in air so he can't move and do one foot at a time.