My car had none of the fasteners when I got it. I too started with a kit that contained all the "proper" snaps, and they were all the short type. When I finished, I found the top would not stay on at highway speeds -the lowest snap; the last one close to the door handle, would pop off on both passenger and driver sides. I got a longer LTD and no longer have a problem with the top coming loose. Since then I have looked at 'original' cars -some swear the long ones are proper and some swear the short ones are proper. I try not to swear, but have a long one at each end, and they work fine.
My car is a pre TS60,000; the locations of the LTDs is different between early and late, so perhaps long are correct for early cars, and short are correct for later. I don't know, but I do know the longer one is needed at the very end -and since it is held in place by a nut from the inside, it is not a quick change from one to the other.