I have replaced the old bearings with new double sealed ones from
McMaster. (made me very glad to have this 12 ton arbor press).

After reassembly, but without any wheels mounted, the grinder runs
very quietly and very smoothly. The shafts do not appear to vibrate at
all. Ie, I can put my finger to the shaft rotating at 3600 RPM, and I
would feel no vibration from it whatsoever. It would feel like pulling
a finger along a flat smooth piece of metal.

However, I if mount those wheels back, they seem to be not
perpendicular to their axis of rotation and make figure eights and
vibrate badly.

I have a feeling that I am not mounting them right.

i