Man, you do have your problems with this bike , don't ya '87!
I feel your pain, the carbs can be a bear to get off/on. I've done it 3 times since I got the bike last spring, carb clean first, then adjustments a couple more times. Anyway, here's what I found that makes it much less of a hassle.
Remove gas tank, aircleaner box, fuel line, choke, throttle cables etc. Loosen and REMOVE the clamps on the upper boots (carbs-air plenum), remove the clamp screws and ease the clamps open trying not to bend them too much.
The smaller upper end of the boots will slide upward a little more without the clamps on. Then with the larger lower end of the boot, turn it inside-out. This is kinda difficult to do, and may tear an old boot, but it gives you a lot more room to get the carbs out. The boot on the left side (rear carb) seems, to me anyway, to be easier to turn inside out, can't seem to get the right (front) boot inside-out when removing, but remove the clamps anyway and push the boot up some.
When putting the carbs back in, turn the upper boots inside-out - easy when loose - and push far up onto the air plenum tubes. This gives plenty of room to wiggle, twist, turn etc. the carbs when re-installing. Pop the lower boots into place, and then turn the uppers right-side out and clamp everything.
I also found it easier to leave the lower boots on the carb for both removal and re-installing. First time taking them off, the left boot stayed on the cylinder head, and the right boot came off with the carb. So it was a boot trying to clear another boot (lower boots). Was a bit of a chore getting one boot out so the other could clear. So when removing or installing, I leave the lower boots clamped to the carb so they stay in place.
So, by the 3rd time I did this it was a lot easier, only about 45 min. removing, and about an hour re-installing. Still a pain, but sure beats brute force like the first time.
Good luck!!!
Gumpy