Unsolvable Woofer Pumping (Phono only)

Since the advent of small, high power, Class D solid state amplifiers and the rise in popularity of home theater, about 20 or more years ago, there have appeared in the market a myriad of small, self-powered subwoofers that typically also have adjustable crossovers and built-in attenuators (so the output can be balanced with that of the main speaker).  Try a pair with your present speakers, which in my opinion are probably excellent, as I have high regard for Focal.  What you are doing is shifting the "problem" (woofer dancing) from the main speakers to the subwoofers, which you can cross over to at very low frequencies, like 50 or 60 Hz.  The result will be a cleaner sound AND more extended bass.  Anyway, that's what I would do in your situation.  I wouldn't necessarily swap Focal for Harbeth, unless you are truly dissatisfied with the Focals for other unrelated reasons.

Neat. I was unaware that that's how they worked.  I'm not dissatisfied with them per sé, just a little underwhelmed in some cases.  A sub-woofer seems like it may be a viable solution though!  One of my potential upgrade paths are the 936s, simply because they have more range/volume.  Maybe a sub would be a viable alternative!
I'm just trying the Harbeths for fun (mostly)...they offered to let me borrow them so I said sure, why not? :)

What about other sources, such as a CD player? If the problem persists with other sources, its likely to be an amplifier problem.

Little pieces of this puzzle keep coming in. I can’t afford and don’t have the equipment to drive a subwoofer...but would a more full range (i.e. floor standing) speaker be a better choice when I do decide to upgrade next?

When the subject is cost-effectiveness then:

Skip the filter, waste of money, won't improve the sound in the least. The clamp will, but only if you get a good one. 

Always in my experience the most cost effective upgrades are tweaks. By tweaks I mean attending to every single facet and component of the whole entire system. Things like Orange fuse, Cable Elevators, HFT, ECT, PHT will bring improvement far beyond anything you can get for the same money the usual way.

You could for example replace fuses in three components with SR Orange, add Cable Elevators, and a full compliment of HFT, ECT and PHT all for about $2k and no way no how will you ever find any turntable or cartridge or anything else for $2k that will come anywhere close. 

Then factor in that these are all "lifetime" in that they will all work wherever you go and whatever you buy forever. Its no contest. Nothing else even comes close.

Also power cords, interconnects, speaker cables, Cones, and Shelf. Same thing. You simply cannot find any component anywhere for say $500 more money that will do what a $500 power cord (or interconnect) (or speaker cable) will do for what you already have. Well, from Synergistic, I should hasten to add. Not that there aren't others this won't work with. I just happen to have 30 years experience that tells me with SR you can throw a dart. Everyone else you pays your money....

Note: not idle speculation- I have TRIED! Compared. Home auditioned. Put a $300 Synergistic Master Coupler on a phono stage, you won't get another phono stage that good (without the pc) until you're into it for three to five times as much. If even then.

My system is heavily tweaked out with all this and more. I've done demo's and removing even one or two of these people notice right away. Heaven forbid I should remove it all, let you hear what the same components sound like the way most people do. Shudder. Cue Brando: "The horror... the horror..."

@psag just the turntable, no other sources!