'83 KZ750 Twin Flywheel Removal Tool?

No, the rear axle, frame head pin, or swing arm shaft will not work, they're all the incorrect thread diameter, I've checked.

What tool do I need to remove this flywheel?

www.motionpro.com/motorcycle/partno/08-0116

Never had an 83 750 twin, but I have pulled the rotor on 76-82 750 twins using the rear axle.

The parts diagrams at kawasaki.com says your flywheel is identical to the 82 model, so 76-80 axle should work to remove it.

Just found the problem, 82 M1 and 83 K1 use a 16mm axle, all the other 750 twins use a 17mm axle.
17mm bolt, probably 1.50 - 1.75 mm pitch (check it) should work.