Not knowing how bad the stains are and integrity of your ceiling material (guessing it's carpet like fabric ? )
Have you tried the Oxy-Clean Method ?
Clean ceiling stains:
"I've had some success removing ceiling stains using OxyClean with Woolite made for carpet cleaning. The only trouble was spraying upwards, it's made for spraying downwards. I did just a small area at a time, sprayed, let set for about 5 minutes, then blotted with clean towel, just as the directions tell you. Does clean it, but very slowly. I'll have to go over some areas.
The Oxy-clean suggestion is a good one. Let it soak a while though. Oxy Clean is a mild bleach and doesn't work quickly, but it is quite safe, even when used in strong concentrations." END QUOTE
-NOTE: I have not personally tried this (Only saving it for a rainy day), but have gathered the information from RV.NET and there seems to be a lot of Positive experiences with this method.
I don't think you would be happy with the finished product of carpet over carpet. Very difficult to trim the edges nicely, and it will almost certainly sag in places if it doesn't adhere properly. This could be a real disaster! Is it really all that difficult to remove the old carpet? Some upper cabinets are installed after the ceiling is done, so you might need to cut around the cabinets to get it off. Replacing with carpet is fine, but also consider a heavy grade vinyl, if the ceiling is relatively smooth.
BTW, the Oxyclean sounds like it might clean your old ceiling. I've used vinegar and water in a spray bottle, and a wet vac to remove it after cleaning, with some success.
If you decide to proceed with carpet over carpet, I suggest contact cement would be your best option.
1998 Triple E F53 with 460 Ford
1995 Jeep Wrangler toad
I have used the OxyClean method and it works . Just mixed it up and put it in a spray bottle, to be able to spray it up into the ceiling. Also used a small scrub brush to work it in let it soak, then draw it out with a wet vac.
I Have had great luck with Oxyclean. Best bet is to lose the carpet and you will lose that issue.
X2, get rid of the carpet, even "clean" looking carpet has a lot of dirt and "stuff" in it! You would be surprised as to the amount of weight that carpeting adds to your vehicle. Vinyl flooring or other flooring can reduce weight keep the RV cleaner and smelling great and looks real nice as well! Good luck!