I'm still a little amazed at how easy that was. The Foley retoother came with carrier bars (separate ones for handsaws and backsaws) and a series of ratcheting bars. As the machine cycles, a pawl ratchets the carrier forward. The amount of movement is set by the distance between teeth on the ratchet bar, and adjustment you can make to the pawl. In this system your ratchet bar is capable of cutting two or three TPI configurations using the same bar.
The trick with getting a retoother is making sure you get the ratchet bars. I got a pack, probably still in the factory paper, but the finest bar in there was 13 tpi. Luckily I have Dad's machine shop for when you have a machine shop, you can do cool things. So I made a 16tpi bar and a custom carrier (the factory ones seemed like major overkill for smaller backsaws).
Because the ratchet bar was a custom length, I had to make a custom carrier for it too. The spacing on the arms is not equal and this was done on purpose to allow me to put in smaller blades (remember the Stub-Nose?).
My carrier and bar on top and factory stock carrier and bar on bottom.
Carrier in the retoother.