"I would like to remove the mirror in order to clean it well. It mounts on a plastic bar that runs the width of the printer. The bar mounts by screws (2) at either end. I am worried that I will need some kind of aligning jig to get it back properly."
The short answer is: DON'T. Some aspects of the alignment are impossible to adjust/correct/reinstall without factory jigs and test equipment. The best you can hope for at home is trial-and-error. Most of the optics is probably solidly glued in place anyhow so disassembly is difficult or impossible - but it doesn't move much either! The long mirror itself is probably less critical than the rest but there is no real need to disturb it.
To clean the optics, use (low pressure) compressed air, alcohol and lens tissue, or as a last resort, alcohol and cotton swabs (Q-tips). However, some lens and mirror coatings may be easily damaged - test in a corner first.
(From: Pete (PTCull@lbl.gov).)
You are correct in being worried. Alignment marks closest to the muffin fan side of the engine should be noted before removal of the Beam-to-Drum Assembly. Better yet, just blow the mirror clean with a filtered compressed air source, leaving the mirror mounted.
Unless the mirror is very contaminated, I really wonder if you'll see the improvement you believe you might? Some of these mirrors have very soft surfaces and only should be touched with lens cleaner or cotton swabs.
If you still choose to remove the mirror from the engine, check to see if the two extreme sides of the page seem even when referenced to the top edge, using the "Engine Test print".