the mounting bracket looks a lot like the one that came with my MityCross. The quick release feature should make it easy and quick enough to swap it over without much hassle.
If you're not willing to deal with 2 minutes to swap over the light mount, I would think it'd be worth the $15 to have two mounts, one for each bike.
I wouldn't advise a hack mount that'd leave the light vulnerable to flipping around the handlebars, particularly on the mountain bike if you're riding off road. $15 is a WHOLE lot less than a trip to the ER because you fell due to not being able to see where you were going.
Should have mentioned that part of the problem is that I have a handlbar bag that needs to come on/off every time I switch out the lights. So it's not just the lights, but also the bag, which is itself somewhat difficult to take on/off. Ends up being a larger production than wanted. Chose to buy a couple of flashlight mounts, will try them.