There's probably a right way to do it, but... a program like RTSS will help throttle the game to 60Hz. Or any other game, to any desired limit.
I was able to externally limit it via the Nvida Control Panel from my GPU's drivers; it's under NCP > Manage 3d Settings > Program Settings and under the "Outrun 2006: Coast 2 Coast (or2006c2c.exe)" options (NOT the FXT2.5 exe) then setting "Max Frame Rate" to 60 and toggling Vertical Sync to On.
I am not sure if this is how I tackled it under the old install, as the program was already there, but it works, and on my first try I was able to get AAA rankings on two bloody hard courses for the first time, so I'm claiming it was the prior frame rate not me that sucked, he he...
I was able to finally get the controls to stick, after getting also hit with the constantly moving menu bug; the issue seems to be the Menu Up/Down input, which was reading input from elsewhere and then being incredibly oversensitive. Recalibrating the gamepad, then try, try, trying again to remap the menu input finally allowed me to get a clean config. I'm still not sure where it's manually saving the actual input, so people can get at them and manually reconfigure (and none of the hacks or mods seem to tackle it either, so perhaps they don't) but my guess is still it's somewhere in the SavedGame folder, as copying that between clean installs replicates the broken controls for both FXT and the default client.