The birthplace of disaster! But covered with good intentions

[Toolmaker51]

Bench grinders are not what they used to be.
First investigate condition of bearings or bushings of motor endbells, for both radial and axial play, it can be corrected. There must be a degree of preload in both axis. Also determine inner flanges run parallel, and wheels are flat.
Test the bare motor, sans wheels, nuts and flanges. Burp or throttle the switch so RPM increases gradually. Insure the mounting or pedestal is bearing evenly on all the feet. A pedestal often responds to bolting down, or a couple felt plies instead of direct contact with uneven concrete floor.
If the wheels are close to being dressed, the problem usually stems from rather inferior products. If density of bonding and material isn't uniform, no amount of dressing will correct it, until the diameter is 'under' the offending internal lump or void.

Worry not.
Make a pair of flanges with somewhat oversize bores, then static balance the mounted wheels. Another technique would be flanges a bit thicker than original, and drill the 'heavy' portions with shallow pockets. If gone a little overboard, those could be filled with lead.