I think Fusion has mill-turn capability and at least 5 axis, maybe more. I've never tried it, I just hand write the mill functions for my lathe and incorporate it into the G code file. Normally very simple 2D milling and drilling with live tooling.
Mach3 will handle 6 axes, so no problem there. You just need to generate G code to tell it what to do.
Use your spindle as the C (rotary) axis, and incorporate the X, Y, and Z into the carriage, or incorporate the Y into the headstock.