"... an old early Garmin GPS that literally EATS 4xAA alkaline batteries in about three hours"

Which model? I've used Garmins for years. I still have my old model 2+ (as well as 2 newer models). Sometimes I take the 2+ on my bike, put it in the bag. Measures distance and leads me back to the place where i started, but no map. Forget about the alkalines. get the new hybrid rechargeables, like Eneloops or other brands. They are great and they hold the charge as opposed to regular rechargeables.

A problem with wireless on small wheel bikes is the wheel sensor is farther away from the handlebar than on a normal bike. I didn't have any luck with the one wireless i tried.

I still remember the old mechanical cyclometers that clicked with each wheel rotation. I guess they're extinct now.