Sounds like an interesting project. After 40 years of battling customers to define requirements for a few zillion projects, I'm moved to curiosity over why one would need the capability to switch from low to high or high to low quickly while it is running -at least on a manual lathe - but as long as you're having fun...
It has more to do with keeping the speed control lever as a go/stop device, than the need to switch speed.

I like the clunky lever. It reminds me of a time before 'Health and Safety', before every thing had to have an E-Stop button. A time when Window-cleaners were allowed to use ladders (you may be surprised to learn that EU/UK law now forbids them to use ladders!!!!!) A time when, when things 'go wrong' it was not always someone else's fault.

I will have my lever - even if it takes 100k LOCs (of machine code) :)