Shooter - Knowing what you want to achieve, I'd certainly agree with you that the LMS power feed is not quite the right answer. For one thing, it doesn't have a rapid traverse button. For another, as it's now on closeout and about to be discontinued, replacement parts or support might become an issue. OK, closeout price is pretty good, compared with the original price. But as you said, the Arduino parts will come out to considerably less. Plus, you get to feed what sounds like a passion of yours!!!
PS - I have one of these LMS table feeds on my HF mini-mill (same as yours), so I'm pretty familiar with it. I modified it to add rapid traverse (basically a momentary switch across the pot wiper). I also moved the electronics to a remote enclosure. This lowers the profile of what hangs off the end of the table, allows me to quickly and reproducibly mount and dismount the motor (it's more difficult to crank the table with the motor attached!), and keeps (conductive!) swarf away from rapidly moving electrons.
As for powering the Z axis, I'd avoid using the existing knob. There are way too many moving parts and linkages for any kind of accuracy. You've probably noticed this if you've ever compared the scale reading on the Z axis knob to what the DRO says. A separate leadscrew or ball screw is the only way to get any decent results.
Good luck ... and be sure to post the details of your final design!