I hate to push this thread back in the direction of traffic safety, but I have a few concerns. First off, never ride on the wrong side of the road. Please don't do it, it's very dangerous to the oncoming traffic, and very dangerous to you. There is not enough time to react, and there is no protocol for reacting. If the car goes off the road to avoid you, do you turn into the road? If the car doesn't swerve to avoid you, what do you do? It's a difficult situation, so don't put yourself into it. The fact that a quadracycle is huge compared to a bike is just making it worse.
You mentioned that you (as a driver) don't notice cyclists at night with only reflectors. That's obvious, reflectors are not adequate for night riding. They are worse than worthless; you need lights. If you see someone riding at night without lights, they are asking to be killed. So don't base your experience on what you see. Get some lights and cars will see you. People are basically programmed to avoid killing other people, so if they can see you, they won't hit you. (Being hit from behind just isn't a common action. Most accidents happen at intersections or when the cyclist is driving incorrectly.)
Finally, I am worried about the width of the quadracycle. Can you share a lane with a car? Will you only be riding on four-lane roads? Basically, if you are worried about being hit from behind, I don't think being a larger target is going to mitigate that risk!
I think you should go for a bicycle (recumbent, of course) or a trike. The trike is almost as narrow as a bike, but you can sit in a nice comfortable position, haul a lot of weight, accelerate faster (much less weight than a quadracycle), and balance at lights. I think if you relax a bit and get some flashers on back, you will love your trike. (I prefer regular bikes, but I see people on trikes all the time, and they are quite useful.)