If you are sure it is the gears, I would be happy to knurl the axle and requarter for you. But gears whine - any noise from a worm gear setup other than a whine is probably due to looseness between gearbox and axle. To test for that, just hold the gearbox with your fingers while on the test stand.
I have a four speed in my ancient convertible Mustang. No vibration when a gear speed is exceeded.
Pittmans are usually well balanced for rotation at rated rpm.