Can't help you with backlash comp. When I've found backlash, I work on the machine and fix it. A camsoft control is worth $10K+, doesn't it deserve good equipment? But, again, this can't be your drift issue. The control should return that ballnut to the exact same spot over time.

Home the machine just gives a repeatable MACHZERO. Without it, your lathe has a different zero position after every power off. I can't imagine running a lathe without homing, all your tool offsets would need to be redone. If you can't install home switches, it is possible to home off a limit switch. I have a mill routine that does this.

Karl