I use Heat 'n Bond Lite for my applique too and I've found that if I only press if for about 5 seconds it sticks long enough to get it satin-stitched on my machine. The few times I've pressed for longer, it didn't want to stick at all. I've heard that over-pressing can cause the glue to become ineffective. I guess it melts into the fabric too much and doesn't allow for a bond between the two fabrics. I might have a spot or two that want to lift, but not bad enough to mess it up while I'm getting it secured.
I've never tried to applique anything with all three layers together. I would imagine that would be too thick no matter what you used. I would recommend appliqueing first on the top only, then layering it for quilting.