There is no way to keep the peace while you're getting things together, especially if every single thing you do sets him off. I was in a relationship like that once, my ex also had severe PTSD from deployment on top of already just being a regular jackass with anger issues. The only way to make it stop is to leave, as you've already stated. You have to step out of your comfort zone in order to leave sooner or just keep putting up with it, which I don't recommend because that shit is draining and you don't deserve that.

He's getting you more and more dependent on him (not allowing you outside, making you think you can't survive alone, making your car undrivable, knows how much money you make/spend) He's slowly sabotaging your success already, that's why you need to leave sooner or else he'll find more ways to keep you trapped.

I know you said a shelter would just make you depressed but I bet getting away from his awful behavior will make you feel so much better. You also have a car so you can lock your belongings (or use a storage unit) so the shelter would just be a place to sleep/shower. If you have a Planet Fitness in the area, get their $10 membership so now you have a better place to shower/hangout with 24/7 access. If you have to temporarily stay in your car until you get an apartment, the gym access is even more valuable.

There're a lot more ways out than you think, his tearing you down is to keep you from seeing these egress plans. You can do this.