I had this issue also when I first changed my plate on my Filco. Are you using the aluminum one or steel? The newer steel ones are slightly loose and wobble around so I don't see why you'd have this issue unless your stabilizer are slightly squashed inwards. The aluminum one was slightly tighter, and naturally bent my stabilizers inwards, so I had to stretch them out with my fingers. This and lube fixed the problem, and now I have perfectly working stabilizers. You might also want to try this. What you want to do is, get the stabilizers out, stretch them slightly outwards so the two arms are slightly outwards or at least perpendicular to each other. Then when you place them into the plate, make sure they are still at least perpendicular, apply some lube, and should fix the problem. If not, then the chances are, the plate may be a lil' too tight on the stabilizer, in which case, you may want to change to different stabilizer pieces because they don't all seem to be the same size.
Cherry mount stabilizers would be a definitive solution, but then you'd have to change to something different, which isn't always the best thing (depending on your preference).
