Note: I'm pretty he does, in fact, cloak like a dick, waiting until you fire at him to do so. If you have dudes on board, /don't fire at him/. (At least not if he has a charged cloak.)
Anyway, that all seems remarkably unlikely, gotta be honest. You said you could take out his weapons, so what's the issue? You have infinite time to take of things after that (on the first form), you just gotta take it easy. Here's an easy and safe strategy:
Knock down his shields, take down his door room. Now send boarders to that room. Fight enemies. If your dudes might die due to cloaking sillyness, just run them around the ship until you can zap them back. If you're doing fairly well, send in new boarders to the door room instead and have the other guys run around leading the crew on a merry chase until you can get them back. Wait for enemies to go to medroom when damaged - blow up medroom, killing current enemy occupants. Move boarders to medroom asap to prevent enemy from repairing it.
Plan takes one missile/bomb if you can take down enemy shields with standard weapons, and 2 missiles/bombs if you can't. If you have rockmen or mantis (or both), your boarders should face literally zero risk in eliminating the entire enemy crew. (Although you should leave the last guy alive)
Also - Have you gotten the crystal ship yet? Crystal crew makes boarding easy as pie, since you don't have to worry about medbay or reinforcements or any of that crap that I just discussed how to deal with. Board 4 space room, CRYSTAL when an enemy enters. Crystal is wearing down? SECOND CRYSTAL. Wearing down again? Let it, get another guy or two in the room, SEND MORE BOARDERS, CRYSTAL AGAIN. Teleport out when finished or, if you're doing decently, the first crystal should be recharged, so repeat.