Is it possible to insert brass tubes through to the mast steps? These would be sticking out say 2 mm above the deck; when satisfied with their placement and the rake of the mast, drop a bit of CA on it to keep it in place.
Sand the section of mast that is the length of the brass tube allowing the mast to slide inside the brass tube easily.
The brass tubes will allow you to insert your masts without stressing that joint on the plastic.