Hiya Blaster,
The main idea to the moist air removal is to take your time,It can take up to a week or more to remove the drawing without damage if you take your time.
Use a towel or clean white T-shirt under the cel to protect the cel from scratches.
I only place the cel/drawing next to the open window at nighttime do to the heat from the sun during the daytime.
each morning very easy go all the way around the drawing and lift the edge a little bit at a time,if you have to pull hard it's not ready to come off yet.
What I do is after each mornings pull, I place 3 or 4 pencils under the edge of the drawing to hold open the gap so the moist air gets to the area needed,this helps alot.
Go slowly there is no hurry to remove the drawing,if you hurry you WILL damage the drawing so bad it can not be repaired,remember the drawing is the real artwork not the cel and should be saved at all costs because it is done by hand and can not be replaced as easy as having a new cel made from the drawing.NOTE* some studios will remake a cel for you if you have the real drawing the cel was made from in the first place,But at a cost!
To me the drawing is worth more than the cel because it was done by the animator by hand,the cel is a copy of the drawing,only older cels were inked by hand and most anime was not hand inked, But there are a few done by hand but these tend to be super high end cels made before the 70s,some hankens are hand inked to this day but they are far and few inbetween as CG has taken over most animation these days.
I was told how to do this by a Disney archiver about 20 years ago and it works so well it is the only way I will remove a stuck drawing, there is no hightech way to remove them that works as well as this does.
I would try this on a cheap cel the first time you do it to learn how it works so you have a better time with the nice cels and cause no damage to them.
NOTE* make sure you dry the drawing for a day or two before you put it back in your cel book or in a bag,if you store it before it is dry you will get mold on the drawing. I place mine on top of the fridge were low heat rises and pulls the moist air out of the drawing,Don't put the cel up there it's to hot for the cel and will cause damage to it,pat it dry with a clean white cotton T-shirt turned inside out(inside is softer) and let the cel sit for about a day is all it needs and then store it the way you do the rest of your cels.
The spots you see on the back of the drawing can be from a few things,I have found that some cels have a black paint over the back of the cel and sometimes this paint is a oil paint used on backgrounds and it can show up as a oily spot on the drawing.
This can also be from the cel being wet by tap water in the past and dryed,Tap water has all kinds of stuff in it and will show up as the drawing gets a little bit moist.NEVER use tap water to clean cels only use distilled water or this can happen to your cels.
This can also be from someone in the past sitting the cel/drawing down on a unclean surface and only shows once the moist air hits it.
I would have to look at the cel inperson to tell you what it is but these three ideas are what happens most of the time.
Graymouser - I have tryed almost all ways of removing stuck drawings and the wet rag or sprits bottles will destroy your drawings and if it has colored pencil notes they will run and get all over the drawings and can not be removed by any means, and some times the colored pencil will bleed into the cel paint and come out on the frontside of the paint on the cel and this also can not be removed once there.
Never let the drawing get to a point of being wet just the moist air will work better than anything else.
I've tryed all the old wise tails like freezers, wet rags, blow dryers,hot clothes dryers,heavy weights on them ect,ect, ect,
all of these will destroy your drawings and some will kill your cel as well to the point of being worthless.
I have found that anything that says it will remove them fast will damage the set both drawing and cel,So NEVER use them EVER.
I hope this helps you out some.
Feell free to PM me if you need to know anything else,I'll help if I can.
Roy

(DBA)Backlotanimation
P.S. WOW Joe you had to go through alot of forum pages to get all those old posts,GOOD JOB!