[Gregory Taylor]

You're stuck with either a 5 or an ultra-6 speed freewheel.

Good luck finding a 5 speed "racing" freewheel (13-22) or (14-24)
.
.
Ultra-6 is going to be even harder to find.

It's even hard to find "racing" 7 speed freewheels anymore. All I have left is a 12-18 and a 13-24 Sachs, and a 12-19 DA, in good shape.
.
.
.

I've had pretty good luck with the IRD freewheels. There were quality control issues with earlier versions - they seem to be gone now. The website gives the stack height for 5, 6, and 7 speed versions, so you can see what might work. These are a pretty pood choice for a bike that is going to be used a lot; no worries over wearing out irreplacable or expensive vintage parts. My 6 speed freewheel indexes nicely with my (non-Ultra) Suntour set up.

IRD Freewheels