Reversing supply lines won't help.
A lathe running forward (M03) normally with a chuck on the left, rotates such that a normal drill will drill a hole, if I can describe it that way.
How many of you have seen a left hand drill? (I have a few!!!)
Old turret lathes often ran the other way (CW) for a few reasons and used left hand drills.
Mostly so the finished part fell into the chute at the front of the machine instead of to the rear.
M03 - CCW. M04 = CW . Normal IMHO.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.