They’re very hard to find these days. You are typically better off buying one that’s already attached to an SKX, usually the Bullet model you mentioned but you’ll pay through the nose for it.
I bought the repro President bracelet from Larry at UncleSeiko a couple of years ago because it tapers like the original. A lovely bracelet but a wee bit heavy. The only alternatives I can think of would be the original jubilee (very comfortable and sits on the wrist like the original President) or try the Z199 repro from UncleSeiko.