You may be able to do a careful, straight knife cut around the panel that needs to come down and put it back without is being that noticeable. I don't remember the headliner in an NL but I think kinda like indoor/outdoor carpet?
The advantage of using new foam (beyond using better foam) is it starts clean with no old adhesive. The fiberglass can be cleaned even with very harsh chemicals, it won't be hurt by it (acetone, MEK, laquer thinner, etc.). The luan plywood will be a little more of a challenge but can probably be cleaned up. You should test whatever adhesive you are thinking of using, polystyrene of both types is quite chemically sensitive.
