Sir:
Grinding a pad is good until you get down to about 1/32 of an inch. Then STOP the mechanical music. From there, do the job by hand with emery cloth mesh, then wet-or-dry paper lubed with water. Go down to 1000 grit if you want a real London finish. Fitting a pad right should take about 6 hours labour. Fitting one wrong will look bad forever.

All best, Kensal Rise