Bill,
If your car had one of the normal grey or black gel coat bodies, I would lean to the paint it side. However, you have an RCR with very nice color in the gel coat. Granted it may not be your choice for the final color, but its pretty darn nice!
That said, no matter how careful you are as you assemble, you will make some booboos. Like FRPGUY, I had someone back into my car within weeks of putting it on the road. Not to mention shooting myself in the foot while trying to adjust the shift linkage by driving off with the rear clip unlached. (Two scratches through the paint and just to the gel. Luckily, that was all)
Even if no bad luck like this should befall you, there will be sorting to be done after you have it on the road. It would be a shame to have to drill holes in a new paint job or some such thing to correct something you found during shakedown testing.
The downside is the difficulty of painting door frames, inside areas, etc. after the car is built. This is especially true of the spider, dash and cockpit. This part of the car has to be affixed to the chassis to properly fit everything else, and really doesn't lend itself to diassembly for painting after the fact. Either way, you will need to have some serious planning talks with your painter. Indeed, he may end up making the decision for you, so to speak.
Regards,
Lynn