Most of the larger frame Cannondales would probably fit you OK. You'd probably be looking at one over 10-15 years old to get the price under $2K. The best tandem I've seen that can be bought new for $2K or less is probably the KHS Milano (Tiagra group, disc brakes).

I'm 6'3" and ride with my kids (5' and 5'6") on my tandem. I deliberately set it up with a big differential in crank length (180mm and 165mm) so they don't feel like I'm spinning too fast, especially given they are not very experienced cyclists. I accomplished that using single bike cranks and right side drive. It would probably be harder with stock tandem cranks because they don't tend to come in as many sizes.

We're still working on the starting and stopping. We started doing this when they were quite a bit smaller and they would just climb on and I would start more or less on my own. After we moved a couple of years ago we got out of the habit and we're trying to get back into the tandem riding now, but the kids have grown a lot in the meantime. The dynamics have clearly changed and we're figuring it out.