So the critical question is: where is "I can hear a relay or contact pop" and "and then something pops" coming from?
The electrical cabinet on the right side and back OR the 2 flexable wireways on the left side and back?
I have had quite a few broken wires in the flexable wire ducts over the years.
An easy way to check is removing the 3 wires on the lower right of your spindle amp (su1,sv1,sw1) and checking resistance betwen each pair (3 checks) all should be well below 1 ohm. This test works best if the axis are in a position like your edit in your last post where the spindle is "dead". If you move the axis, the broken ends may reconnect and show good on the test, and it will run sort of...
In the case I have described above, the "pop" is arcing at the point the wires are broken, or at the point that the insulation is broken and arcing to ground. This happening on a repeated basis may cause problems in the drive, that will give a hard alarm that will not clear.
If you are rehoming the machine at power on, after cycling power because of the "pop" and sometimes it will run again. The movement you are doing may be enough to reconnect the broken ends of the wire(s).
Normally the 5 digit display on the spindle amp would have some display after the "pop".
"From what I read Makino had two spindles motors available; 45-4500rpm standard and an optional 60-6000rpm." This may only be a change in the pulleys on the motor and spindle and both using the same motor. There will be parameters that differ also.
Bill