One way is to use a 3 way switch and wire it like a Tele with a master tone. Then the spare pot (previously tone) can be used as a volume for just the middle pickup. That way you can introduce the middle pickup to any setting. I used that system for years and really loved it.
The problem with swapping left and right handed parts is that the pots have a logarithmic sweep. So if you wire them the other way the volume won’t work evenly.