I think there are much bigger issues than ohmic sensing from what you describe, namely bad wiring/shielding/grounding in general, so my strong advice is:
-do not fire the torch before grounding things properly
-make sure the power socket and the machine are grounded and the shop has proper ground rods
-make sure the PC is grounded
-make sure the plasma source is grounded
-disconnect anything ohmic related from Mesa
-disconnect the THCAD from Mesa
-connect THCAD only to plasma source
-wire and test the new Mesa, make sure everything works properly, wire the Torch ON to plasma source
-power on the plasma source and cnc machine and start QtPlasmaC or PlasmaC or whatever you are using
--enable LinuxCNC, jog around a bit, then use the Torch PULSE on screen set to 1 sec (default) ONLY ONCE !!!!!
-did anything move/burn/make strange noise/screen blank/PC turn off or lock/Mesa reset or lost connection/THCAD smoking ?
If any of those is yes, turn OFF everything and go back to wiring/shielding/grounding (goggle Hypetherm grounding they have a nice general guide)
If all above are no, try the pulse again and again, waiting 5 seconds between, make the pulse time 3 seconds and test several times again
If all that goes OK, try to do some manual cutting (use F9 to probe and fire the torch then jog manually), do several short cuts
If all good, power down and wire the THCAD to Mesa, do the same procedure from the line with two - signs above
ONLY if all tests go without issues proceed to wiring and testing Ohmic sensing. Again test from line with two -