I've rattled vinyl, most of the time I'd just airbrush it to make it look nicer. Backgrounds, I'd use combinations of weird stuff from seran wrap, alimunium foil, rattle cans with cut tips (fans it differently), tooth brush bristles, and some other improvised stuff to make rock looking backgrounds, marble, etc.
Painting foam or 3D Letters without a spray booth, have you considered painting them? I had to do 3ft NAPA AUTO PARTS in HDU foam. When it came time for color, I just painted tight spots and feathered it out far, then came back with a foam roller later. Course, I used One Shot. It came out without peel or dry spots.
Painting a nice solid color background, of just the base color of what I'd work on for those improvised techniques? I'd still roll on the paint first. Spray paint cans are just made to do joe blow jobs. Paint screw heads, mark tools, or spray paint small items. You can make it look better by adjusting what angle, and distance you spray from, always turnging them upside down at the end and spraying til no paint comes out (clears the head of excess paint that will dry and foul it), or use an exact and cut into the nozzle a bit. do it wrong it'll drip though. Still, in the end, it's a cheap alternative.
Personally, if you are comfortable using a spray gun, I'd see about trying to get a smaller paint booth where you are already at. If that's out of the question, you could always do what old automotive repair places did and wet the floor approx 6ft outside of the area you'd work in then pain. I'm sure the EPA wouldn't like it, but most automotive places are highly regulated due to Laquer paint which many of them still use which you know from experience is a pretty hazardous material. Spraying... a latex on a house is totally legal though. So it's not really an issue of spraying paint without a booth, I'd look into it and see if you could legally spray with the type of paint you intend to in your area.