The qualities of the car that are in your favor are the (hopefully accurate) low mileage, the (probable) originality/lack of 'customization', and the indoor storage after an event-free road life. Things not in your favor are a (probable) lack of on-going maintenance or proper 'put-up' for long-term storage, and not being driven on occasion. (Being driven really matters to cars... plus it's what the car is all about.) But as others have mentioned, settling on a value depends entirely on the marketplace. You have mileage and condition that few other cars can touch, but there are many cars available that a buyer can just get in and drive today, and for years to come.
Then, there's kind of a sense of 'obligation' that sets in. What should be done with this car? Preserve and drive responsibly? Or view it as the fastest way to a V6 conversion? Tiger 'clone'? Everyone's going to have a different take on this one. These cars are not exceedingly rare -- like there are just a dozen in existence worldwide. But they're not making any more of 'em, either. Ultimately, whoever owns it gets to make that choice, and your control over the plans and dreams for that car ends when you sell it.
Were I in your position, the first thing I'd do is arrange to meet with a few of the club members, or any Alpine owner, and go for a ride/drive in a well-sorted-out Alpine. Top down, nice day, good road, not in a hurry, etc. An afternoon of that will go a long way to clarifying your thinking about the car you have. Mull that experience over a bit. It would also be interesting to have a similar ride in a V6 and or V8 version, to see what other factors can influence the 'fun to drive' rating.
Then maybe drive an Alpine again, just to calm your nerves.
Technical help, parts, advice, etc. are probably easier to come by now than when your car was being driven. (If this car is to be turned over to a new driver at 16 years old, then don't put a V6 or V8 in it... I'm sure you'll end up regretting it. )
Well, I'm rattling on now, but do try to meet up with some folks (and cars) in person. It'll be time well spent, regardless of what you do with your car.
Ken in Columbus