I use one of the old off-white Woodcraft no-name bench grinders, a Rikon 1/2 hp and a Rikon 1 hp, all half speed. The 1/2 hp is a bit under powered. I use an aluminum CBN wheel and a metal polishing wheel on it and it spins up OK. I've heard that someone with two steel CBN wheels had to give his some help by hand to get it started.
Before I gave up on the old grinder, I'd check the shaft with a dial indicator as someone mentioned, or a dial test indicator. If you don't have one you can rig a pointer indicator: rest something like a yardstick or longer on the top and near the end of the shaft, hold the end of the stick firmly against something to make a pivot point a few inches behind the shaft, then have someone rotate the shaft by hand while watching the end of the stick. Any runout on the shaft will be amplified and visible on the far end of the stick.
Also, check for side-to side runout on the both wheels. Perhaps a wheel was rotated some and the washer is not perfect
. (I like to use the inexpensive spherical washers from Woodturners Wonders when mounting CBN) You might try mounting a different stone wheel if you have one.
I assume the vibration is not from something as obvious as a chunk of wheel missing after the crash. Does it run smooth with just one wheel at a time?
If the shaft is bent it might be repairable.
As for speed, I think the lower speed is best for hardened high-carbon steel tools to help prevent overheating. HSS and 10V tools can take the heat. However, I like the feel of sharpening with the 1/2 speed.
JKJ