IF it has the capability of mounting brakes F&R as @JohnDThompson noted why not equip a 3spd IGH as was traditional on many British path racers pre-WWII?
Sturmey Archer even makes a FG/IGH, the S3X for the adventurous.

Note that many of us have perfectly usable FG and IGH machines that see considerable service in either configuration, properly equipped with brakes and foot retention like any road bike.
Which raises another point. Track bikes are designed for use on a Velodrome and make miserable road bikes with a lumber wagon ride on rough surfaces, twitchy handling and nervous descending.

As always, suit yourself.

-Bandera