I'm surprised that you're having trouble with the Testors MM Acryl paints and masking.
Just last night I was painting the alierons for my F-4. I rolled some regular masking tape into a tube with the sticky side out and stuck the kit pieces to a piece of heavy cardboard with the tape. I shot a coat of flat white on the pieces and then ran my wife's hair dryer over them for a few minutes (on the low setting). I shot a second coat and again did the hair dryer thing.
I then turned the pieces over and stuck the painted side down on the tape and taped them to the cardboard. Two more rounds of painting and drying and the pieces were ready for me to paint the red edges by hand. The total elapsed time was about 30 minutes or so.
The important thing was that the masking tape did not pull the paint off the pieces. In fact, I've done a lot of masking on this model and not had any trouble with paint coming up.
I did, however, spray the whole thing with Testors enamel flat light grey from a rattle can for a primer. I found the MM Acryl paints laid down very nicely over the enamel primer, but I let the primer cure for something like a week and a half before painting with the Acryl paints.
The parts I worked on last night weren't primed.
Maybe a good enamel primer will help.
Regards,
-Drew