Years ago, as a desperate teenager, I had my Sears 3-speed frame converted to a track bike. A friend of the family chrome plated the frame after polishing the track ends to a mirror finish.
No matter how hard I tightended the nuts on the rear hub, one side would always slip until the tire rubbed a chainstay.
The only way I found to resolve this problem was to install chain adjusters (Part No. 381, Cyclo-Pedia, 11th Edition).
Later I noticed that I wasn't the only one riding track bikes with chain adjusters, especially on the road.
Chain adjusters were once common on British utility bikes.
Don't know if and when they were common on track bikes.
Amir Avitzur
R", Israel