After pulling some more shots with the newly sound insulated Anita, I've realized that the pump didn't turn off the other day in the middle of pulling a shot. Actually, I think what happened was that it was so quiet, I didn't hear it and thought it was off.
Pulling shots last night and this morning, I found that the pump starts out somewhat noisy, then goes almost completely silent when it goes to full pressure. Sometimes the OPV opens, which makes a comparatively loud chirping noise, but if the OPV isn't open then there's virtually no sound at all. Amazing. I had no idea a vibe pump could be that quiet. Now if I could just get the OPV to stop making that annoying chirping sound, the machine would be almost totally silent under full pressure. Maybe later I'll post a video with sound so you can appreciate how quiet the machine really is.
Oddly enough, the pump is still pretty noisy when the boiler autofill kicks in. I've noticed before that the autofill is always much louder than the sound the pump makes when it's pulling a shot. Not sure why that should be the case or what to do about it. Still, it's nice to reduce the noise as much as I have so far.
The bottom line seems to be that $15 of Dynamat sound insulation and a $7 sink protector plus some electrical tape can actually make a real difference in the sound level from a vibe pump machine. Amazing.