P38 is unlikelyto stick to Styrene but abraided like you have, it should hold the stuff you pug behind well enough letting the epoxy do the sticking.
Styrene is like any material, misuse it and it will let you down. Try and keep finger grease etc off the plastic when glueing as then the bond will be better and remember that thin styrene can soften and distort if using plastic weld or styrene glue, but it can be used to make curves and rings laminated around a former.
A scalpel will cut styrene up to around 1.5mm after which I reccomend a Stanley knife. Snap the thicker styrene carefully and dress the edges with a sanding block/ file, blade run along it until square. Annoyingly there seem to be two types of styrene possibly made by different companies. One has a tendency to break unevenly when snapped. This is a bluer colour white, while the yellower white styrene is easier to use but has wonky edges that have to be dressed before you can measure and cut accuratly.