Below my alternator regulator where the wire harness attaches next to the radiator there is a clip. In the assembly manual page E8-1115-1 View A there is supposed to be a wire strap item 6. I've attached that view. In my instance there is a white inline wire clip that is a part of the wire wrap. My clip is broken. So I replaced it with a strap but the hole is too large so the strap won't remain in place.
Back to your original problem, the specified strap, 376914-S, as specified in the 1968 Mustang Electrical Assembly Manual (AMAM0023) page 8, Ford drawing E8-8115-1 (since corrected), view A, is what I would expect to be used if I were judging your Mustang.
You state the mounting hole is too big and the strap "won't remain". That is an indication of two situations - the mounting hole is too big, or the mounting "stud" is too small in diameter.
Solutions:
1. Make the hole smaller. This is not as difficult as it sounds, if the car was going to be repainted. With a torch and two ball peen hammers, the mounting hole could be heated and "deformed" enough smaller to retain the "stud". It's a technique I've seen done at a local body shop for sheet metal screws that have "stripped their mounting holes.
2. Make the mounting "stud" larger. In this case, cutting a slit about 3/4 of the way up the "stud" with a very thin saw, thinner than a hack saw, or a "Dremmel" cutting disc, to make two "tabs" and then prying apart the two "tabs", will make the mounting "stud" larger in diameter. This "prying" could be done before the strap is installed, or after, with a small flat blade screwdriver. If you apply some 3M8008 or 3M08581 black weather strip adhesive, then cover your "artwork" with undercoating, it will hold (and I won't tell). If you think the strap might still come out, cut a tiny wedge from another mounting strap and inset that into the newly cut slit, then apply the adhesive. This will work if in the near or distant future, the strap is not intended to be removed.
(Think outside the box.)
Jim