...Any layer added to the panel which gives rise to a significant change in the total mass of the resulting construct will cause significant change in the bending moment of the panel and thus its resonances.
...Stiffness is a fine thing in a plywood box... - but don't let that stick you with the idea that bracing cabs is the beginning and end of vibration control. ...Constructs of extraordinary stiffness [and mass] can ring like a bell.
For example: bells
Dynamat or similar materials, in addition to the damping effect of the visco-elastic properties, add significant mass to the panel - typically from about a quarter up to about a half a pound per square foot. If you add that much mass to a sheet of half inch plywood the resulting panel may approach an overall doubling in mass! This is a BFD fom a vibration perspective. ...If you care stand the weight penalty visco-elastic layers are a great way to reduce panel resonance - especially so in a constrained layer format. In fact in some cases this approach is the lowest weight solution.
Bill keeps advising people with vibration problems to ignore everything but panel [box] stiffness. This is bad advice and pretend physics. In the automotive and aviation industries visco-elastic materials and constrained layer constructs are standard approaches to vibration problems - and it aint because they just aren't clever enough to make a stiff panel.
This is probably all good science, but IME, Dynamat would be just as irrelevant as paint vs Duratex or carpet, at least in any practical way with regard to a fEarful used for electric bass.
I've used Dynamat to great effect to reduce ringing in thin unbraced metal and/or plastic panels (car roof, doors, hood, and plastic motorcycle luggage). The difference was immediately audible, changing the sound of the struck panel from a sustaining, high-pitched "ping" for metal, or a more muted drumming sound for plastic, to a dull, short-lived knock.
But the half-inch plywood in a fEarful has more internal damping than a car door. Also, the unbraced areas are much smaller, so any undamped resonances are happening higher in the audio spectrum, where they have less relevance to us as bass players.
As far as I'm aware, there isn't a conventional, decently braced wooden cabinet on the planet, that rings like a bell (or even like the roof of an old Honda Civic). Since we're not hearing sustained, bell-like musical pitches when we strike the panels of a fEarful, there clearly isn't the same need for add-on damping.
Also, we're talking about a bass cabinet, not a high-end home audio speaker. Dynamat might add a subtle improvement to the clarity way up high, but how much energy are we putting into the structure at 5K to 20K? Not a heck of a lot. This is one of those technical differences that might be measurable with the right test equipment, but would be meaningless on stage.
Finally, the original question was about finishes, not about lining a cab with Dynamat. And as Foz admitted, none of the suggested products carries enough mass to make a pinch of difference.
Seems to me that Bill FM is still right, at least for our purposes as bass players.