This is getting to be a tougher and tougher decision to make as the decreasing number of cars going through restoration is driving down both the prices of project cars and parts. There's been a decent 71 for sale down here for months for the high $2k range and it still hasn't sold. It's a 318 Sattie but in really nice shape, but the market for projects is going down since there are so many finished cars on the market at decent prices it's not worth investing in a rough project for anything more than a grand or so.
The outlook is a little better for parts, but even those seem to be getting harder to sell, especially the more model-unique they are. For example, there's a larger market for an 8.75 center section than for an entire rear end, and there's a larger market for an entire rear end than for a set of 71 RR seats. And there's a larger market for the seats of a 71 RR than for a grill off the same car. The other issue is there are a lot of parts being dropped into the market as people who had been holding onto them for years are trying to cut their losses just like car owners are.
The other hazard of parting your car out is it's unlikely you'll find buyers for a majority of the parts, and the more parts you sell the less likely it is someone will buy the whole car and you end up with a car with no drivetrain, missing a door, trunk, wheels, etc., and nobody wants what's left and you end up letting it rust away in the backyard or selling it for scrap.
I would suggest taking a few months and try to sell it as a project car and just ask a decent price for it.