Thanks for the replies.
I realize now I should have given approximate dimensions. I made a quick sketch of what I imagine the crimp/rivet/spot would have looked like before it was put into the strap. I drew two side views and a top view in PS so hopefully you get an idea of what it would look like in 3d. As I labelled, the diameter of the top is only 3/16", and I imagine the "arms" that pierce through are around 1/4" to 5/16",since they are long enough to go through the leather and back over the string the full length of the top again.
Based on your recommendations, "spots" seem to be the best option. I have 2 concerns with them though. First, I'm concerned that they will not be strong enough to tightly crimp the string. As a saxophone strap, they have to withstand at least a couple times the weight of a saxophone (ideally more), and whatever crimps the string onto itself will have to keep the string from budging under that kind of tension. My second concern is that they seem to be fairly hollow and rounded on top. This means the will stick out a bit far (not that big of a deal), but also they won't have much metal in contact with the string that goes on that side of the leather, which would mean less force holding the string in place (force = pressure x surface area). I fear when I crimp it, it might cut into the string, weakening it. Because these "spots" appear to be for decoration I'm afraid they won't do very well as a load-bearing piece of hardware, unlike rivets, crimps, or eyelets, which are designed to withstand notable forces. I'm also having trouble finding any 3/16" diameter ones, and because they are only designed to hold themselves onto leather, the "arms" all appear way too short in relation to the diameter of the top. Whatever I use has to be long enough to pierce through 5-6 oz leather, then fold all the way over another 3/16" to fully wrap over the string on the other side...[10 minutes later]...I added a quick sketch of what it would look like if I cut away the leather (and half the eyelet) to be flush with the side of the crimp/rivet/spot in the original strap. Hopefully you can get a better idea of how long the "arms" have to be, and why I'd rather the head of the spot be flat on the bottom as opposed to concave. Actually I just noticed hivemind's pic, and those spots could probably be hammered flat before I attach them. Do you know where I can get spots like those?
Anyway...sorry to be so particular in what I'm looking for. I don't want to sound anal, it's just as an engineer I'm concerned about the forces involved if hardware not intended to bear heavy loads is used. If the hardware crimping the string comes loose at a bad time, I end up with a massively dented $7000 sax. I also might try simply fabricating some 20 gauge steel into the appropriate shape, or something similar. I'd obviously prefer to use a piece of premade hardware simply because it would look nicer, but if strength is an issue I'll see how ugly it is with a hand-made steel crimp.
If I can't find something strong enough and whatever I can make ends up too ugly, I have another method of attaching the string, but it doesn't look as nice, nor would it be a replica of the strap I'm trying to copy. I really appreciate all the advice, and if anyone knows where I can find spots like in hivemind's pic (assuming I can get 3/16" diameter), let me know. Ideally I would like a flat-top spot as opposed to the big dome on those, but if I can get them for cheap I may try them anyway before I rig up something out of sheet metal. I'll do some testing on whatever I use before it goes into a usable strap, it's just that I don't want to waste a ton of money trying 5 different things just to make 1 strap for now. Thanks!
i hope my train-of-thought method of posting was understandable