Hi Max,

Yes, getting the S3X will give you three fixed gears. There’s more lash (movement) at the pedal before engagement than with a straight fixed gear, but you can have a 60” and 70” gear to complement your 94” gear. It should be much easier to power over the bridge, and you may find that the 70” gear is more enjoyable for non-racing riding than the big one.
This would keep the same 50 ring and chain you currently have, along with a Sturmey-specific 14t cog. You would need to run the shifter cables somehow..

This hub allows for a freewheel to be mounted in place of the fixed cog, as well, so you could try out coasting on the same bike.

Other multi speed fixed options would take too much time in a race, especially if the course crosses that bridge 6 times!
I have a fixed gear with two rings and a double cog that I shift by dismounting, loosening the rear wheel, dropping the chain to the small ring/large cog, and retightening the wheel. Takes 15 seconds, which is nothing on a recreational ride, but everything in a race.

The other option mentioned here was the Sturmey S2 kickback hub. I have one and like it a lot. You would need a 20 tooth cog with your 50 ring to get a high gear in the mid 90s. The low would be 67” which could work. You’d need to lengthen your chain.

Philip
Santa Rosa, CA