Hurst motor rumble?

I'm confused. Why would you even "drop the stylus onto a stationary object next to the platter"? Unless you are cleaning the stylus and if you are you should mute the preamp.

Then you say to perform the test "you need deep bass". So are you actually playing a record? Nothing in your post states that this happens when you are actually playing a record?

If this doesn't happen when a record is playing, what difference does it make? Granted, it would probably drive me crazy too, but if it doesn't happen with normal use, let it go.

I just tried this on my custom HW-19 and it doesn't do it, but again I'm not sure that I completely understand?

The rumble is masked by surface noise when a record is played. As we all know, unheard vibration can cause audible effects elsewhere.
The fact of this vibration getting into the signal matters, I would think especially at higher volume.
It is irrelevant what I should or should not do when placing my stylus on a plinth mounted cleaning device. The fact of the rumble remains.
The vibration is clearly low-frequency. That's why I suggested you would need speakers capable of some bass. Also, since this noise is pretty low level, you'd need, in all probability, to turn up the volume to hear it well. I listen at pretty high volume but this noise can be heard (but only with the belt in place!) at low levels, also.
If you tried this test on your "custom" HW-19 with negative results with the drive belt connected and turning the platter and the needle resting on something attached to the plinth but not the platter, like a stylus cleaner, and your speakers reproduce 60hz signals and you tried the gain at high, then I conclude that my problem is solvable with a motor that has less vibration.
This is what I am trying to determine before putting money into it.

The secondary question, then, becomes what motor can I get at reasonable cost that has lower vibration than the standard Hurst 600RPM motor.

I know that VPI is now using a custom made 600rpm motor.
Still from Hurst, but not available from Hurst directly as a
replacement, you have to order it from VPI. I've read that it
is supposeably better, (not sure in what regards). You
could contact VPI and ask them.

Two suggestions.

1) install a rumble/subsonic filter http://www.kabusa.com/rf1.htm

2) try isolating the SAMA better with a compliant material like sorbothane. It is possible that motor vibrations are being transfer to you table via the platform.

It's hard to figure out what is going on.

But if you want a quieter motor, you can try the 300 rpm one. You can get it less expensively directly from Hurst (IIRC it's exactly what VPI uses) but you would have to get a new, larger, pulley from VPI.