So I finally got around to checking out this tire with the nail embedded. After talking to a local Bridgestone tire shop, they confirmed that the RFT can be repaired as long as the tire was not driven a long distance with low pressure. They did warn me that removing the tire from the rim can be a real pain given the low profile and general inflexibility of the sidewall in a RFT.
Today I swung by the shop with the wheel just to get their advice. Interestingly, while the car was stored over the past 3 months, I inflated the tires to 50PSI to try and avoid potential flat spots etc. The tire with the nail had not lost any pressure over the 3 months. That seemed strange.
Well it turns out, the absence of pressure loss wasn't so strange because when the object was removed, it turned out not to be a nail at all.

The little screw was embedded but wasn't anywhere near long enough to puncture the tire. EXCELLENT!!
Here are some shots of the tire tread remaining on the tire. It is between 5-6mm depending on the position so I think I'll be OK for another summer season on these tires.


