[MAG]

Safety first here. Don't forget to fasten your seat belt. They are installed...right?
The roadster latch design is not the strongest mechanism employed. There has been a lot of "hammering" applied to the latch plate and assembly over the years. Wear is very common to these parts. If the dove tail as well as the rubber bumpers are not in place their lack of support makes the problem worse possibly causing the door to fly open. This is no place for a band-aid repair.
The Heli-Coil as suggested might work but it would be best, as you mentioned, to remove the upholstery and make a proper repair.