I had/have a bit of a crazier bridge rattle issue on a Fender Jaguarillo. It has a Jazzmaster style trem, but the bridge is a tune-o-matic style. It had one saddle that rocked side to side when the string was vibrating. This not only caused a noticeable buzz sound, but was also a significant sustain killer. I talked to Sweetwater and Fender about it. Fender said they'd send me a new one when they had one in stock, but they never followed through. Bastids.
Sweetwater took a bridge off a Jaguarillo they had in stock and sent it to me, but it had even more saddles with the wiggles. So far I've given it a "high-tech" solution of shoving a bit of common staple wire on the side of the saddle so it has no room for movement. Not a great solution at all. It will probably eventually fall out and I'll find it some day stuck in my foot, but it's working for now.
I occasionally look for replacement bridges, but I have this conundrum of wanting to find a replacement bridge that has a 9.5" radius to match the neck radius. I don't know what the radius is on the stock bridge, possibly it's also a 12" like the replacements I see, but for right now, the staple wire is working. LOL