So he has a BiPAP he's not using because the settings may be wrong? That is not uncommon. What model is it? I can tell you how to adjust it and suggest a starting point for "start low, go slow" settings.
The parasomnias you mention when he is sleeping could easily be related to insufficient oxygen, which the BiPAP is designed to help at this stage. For example, the active dreams and kicking could mean that his subconscious is trying to arouse him (possibly to breathe in the air his body is lacking).
The shaking is concerning and if nothing else expends energy he doesn't have in reserve, suggesting that you really might want to move the BiPAP up on your list. It only takes a couple of minutes to adjust. If the shaking persists once he's on BiPAP, it would be time to look at things like diet and hydration.
What kind of wheelchair does he have? As Mike mentioned, you definitely want to keep changing up the tilt, and I will add, make sure the arms/shoulders are supported, esp. with a history of lumbar injury as you mentioned. We used foams and pillows, way beyond the wheelchair arms, which were only a foundation for the elbows, which also had foam support.
Everyone has had great advice. Ocean County is one big destination as I'm sure you've seen...you'll have a lot of fun outings there, once you get past all the domestic moving madness. Just take one to-do at a time.
I would certainly contact the ALSA chapter that covers Ocean County and see what advice they would have (from what I remember, the clinics that way are pretty widely spaced, e.g. Newark, New Brunswick, Philly, unless I am forgetting one; my husband was diagnosed @ Penn, so that one I know), assuming this move is in the fairly near future. And you might keep NJ Transit access in mind when planning your new rental; the winters and traffic may make you happy to have that access at times, even if you aren't normally transit passengers.