Oh yeah, it requires you to remove the back all right. Not a bad idea to use a large mirror as you're adjusting also. There are several convergence adjustments that need to be made on the yoke of a picture tube. They're ALL glued as to not be shaken loose, but as quality control has progressively blown chunks throughout the years (can you say unfair_trade_practice or 'sweatshop'?), I do not recommend just anyone try this though. Major shock risk if you've never attempted before and/or are a clumsy oaf. Here's some great info in layman's terms what we're talking about:
Linky to monitor FAQ's
My first 1080 was one that was damaged when shipped to one of my friends VIA UPS and they ended up paying him for the damage but not collecting the monitor. He gave it to me and I was able to repair the main circuit board which was broken right in half. The convergence was way off (not sure if that was even related, like you said could have been factory because it was glued) but i managed get it perfect by pure trial and error, but at one point i thought i'd never get it correct. I was wearing rubber gloves because i was afraid i'd be electrocuted.... not sure if that is necessary.
before that i was using my A500 with a amber composite monitor. Terrible monitor for an amiga, except for interlace mode which had almost no flicker.