I dont see any issue with putting all the tuners on the bottom (right) side of the head stock. You may or may not need to employ some string re-routing options (eye bolts), but should work fine if you have room on the head stock and your break angles (over the nut) are decent. Obviously, the tuners are not reversible, but you seem to know that if I understand correctly.
Well, do what you want but you could look closely at the tuners you have on hand and decide for yourself if it is possible to:
I think you will be pleased with your discovery. :D
The worm is the part you turn engaging the gear which rotates the shaft affecting the string tension.
Take a breath, relax and simply put the thing back together.
Refer to one of the other tuners if necessary.
The only difference will be the end of the worm will need to point in the opposite direction.
The Capo Kid has pictures of the results in the thread concerning Shane Speal tuners.
This process is simple and you can do it.