Lampoon, I think your estimate of 3000 made is pretty close. But I think you are way low as to how many remain. Consider that the early GTOs were already being talked about as "collectible" by 1973. Convertibles considered the "most" collectible.
I forget the statistics for all vehicles, but a pretty high percentage of '65 GTOs would have survived into the early '70s according to Gov't estimates. The annual scrappage rate was a lot higher than today, I think about 10%. But even after 8 years at that depletion rate, there would have been about 1200 still on the road and many that weren't, were not yet scrapped.
They were driven hard and abused, especially by young owners when they were selling for cheap as 10 year old cars and many were probably destroyed during the early to mid '70s. But since they were thought of as collectible, people didn't scrap them even when they fell into bad repair like they would have with a run of the mill 4 dr sedan for example.
So I think you'd lose that bet. More like 750 to 1000 is my guess. Still just a guess, just explaining why I think hobbyists misjudge the survival totals.
This one isn't a convertible, but I spotted this while looking for stuff on the "Tonto VI" Collingwood Motors drag racer.
Scroll down about 1/4 of the page for "then and now" pix of a '65 GTO hardtop with 4 spd and Tripower. This is an example of the kind of condition a lot of "surviving" '65 GTOs would be in today that leads me to believe the no. of 4 spd, TP, '65 converts is much higher than 250. JMO.
http://www.codyhotrodshop.com/VINTAG...0-S--70-S.html