I've installed a new stopbar (TP-6 fine tuners) on several Heritage guitars from the period and ran into the tight spacing.
The solution for me was buying studs out there that were used on/sold for the Les Paul Custom (LPC), which have a slight dimensional difference from those used for the standard. I would actually buy the stopbar, which came as an assembly, to get the LPC studs and toss the bar itself.
As I recall, and this is 15 years out, they were Imperial so someone may have swapped bushings when the original bar was put on your guitar. Heritage would do a lot of special orders at that time.
I don't know if this is what you are running into, but it's food for thought and worked to solve my problem.