suggestions for how to implement a weird VFD jog mode?
The advanced manual for your drive is here:

https://inverterdrive.com/file/Commander-SK-Advanced-User-Guide

This drive has the capability of a ladder logic program running in the drive. This is probably how they implemented your unique jog function. 

To run a ladder logic program, the drive needs a special memory card called a “LogicStick” that stores the program. Did your old drive have this LogicStick in place? If so, it is entirely possible that the program is still intact on it. Try moving the LogicStick to the new drive. 

If the program is not retrievable, then you’ll have to write a new one. It is outside the scope of this site to write that program for you, but if you have any specific questions while you work on it, you can ask them here.