Proxxon MF70 Anti-Backlash Nut

I try to eliminate the Backlash on my MF70. I came with the idea of "tightening" the threads. I plan to hand tap with a M6 6h tap.
The rod is a 12mm brass rod and replace the PTFE nuts.
This Upgrade implies to change the 6mm left threaded rod for a right threaded one.

Please share your thoughts. If you think it could work, i will try to make it.

PS.:That's not the real mesurments (the holes are too big, it was just a 3D clearence test) it's just the idee, the way i would do it.
I didn't test the fit.