If I remember correctly my '67 GT did not have a laminate. I believe it had a printed, textured vinyl covering on the doors and cabinets in the bathroom. I recall re-glueing down the loose edges.
I'd start with something benign like Goof-Off or maybe even Goo-Gone on a small area and see what happens.
AirForums # 2806
WBCCI / VAC # 6411
Not All Who Wander Are Lost.
Avid supporter of trailing edge technology.