Hi,
there is no such thing as a USB-to-parallel converter that works with Mach3, it manages to lose all its critical timng.
My suggestion would be to replace the existing controller completely.
Given this is a new project then I would use Mach4, all development on Mach3 ceased seven years ago, whatever bugs it has its stuck with.
Nor would I bother with a parallel port. The parallel port was the only viable, cost effective solution in the early 2000's but its to limited to be considered
a good solution today when the cost of external motion controllers has come down so much.
I use Mach4 and an Ethernet SmoothStepper and a home made breakout board, but one or more C10's @ $23.00 each are perfectly good
breakout boards.
Craig