You are correct in most of this. Seated, I do use my hams exactly as you say, but that and the hip flexors are enough to pedal seated without quads, just as one can also pedal only with quads. When I start going hard again in the spring, I'll sometimes cramp - sometimes quads, sometimes hams, sometimes both, so I know I'm working them fairly equally. But I don't think I've ever cramped a hip flexor. I used to do straight legged deadlifts to strengthen my hams because they are hard to work. That helped some.

Yes, it is poor technique to bring the rear wheel off the ground. It's a matter of eliminating or correctly timing the body's up and down motion. It's tempting to want to raise the body up so as to come down with maximum force on the downstroke (bobbing). However if one is also pulling up hard on the backstroke it's easy to bring the rear wheel up, if not the whole bike. OTOH, one doesn't want to not pull up because that robs power. So it's a matter of controlling body motion.

It's sort of like following through in other sports. The backstroke foot is still pulling up hard when the pedal reaches TDC. If the body is also coming up, the bike comes up, too. Because the leg is extended when standing, the muscular geometry is different and the hamstring can exert a lot more force than when seated. I was just using that as a way to show that riders do in fact pull up on the backstroke, and pull quite hard. It sure isn't the downstroke foot that's lifting the bike.

Stoker and I went up one of our local short, steep hills this evening, out of the saddle at maximum force. We were pulling up very hard (as well as pushing down!), but trying to be as smooth as possible. We were just barely maintaining traction on the dry asphalt even so. Tandems are a lot of fun.