Well, that's an interesting read to date. Some well thought out points & counterpoints. So here's my take based on a lot of A - B testing & experimentation, but, of course, it's not straight forward, & there's numerous caveats, so belt up for the ride
Background stuff
Head resonance is distinct & separate to shell resonance, although their functions are always linked together. The heads produce almost all of the drum's sound, but the shell shapes that sound. Think of a drum as a speaker cabinet: the heads are the speaker cone, & the shell is the cabinet material, dimensions, design (baffles, etc).
Ok, that's the concept layout, let's look at functions. The shell shapes sound via two mechanisms. 1/via sympathetic resonance (the same way your ear works), and 2/via acting as a conduit for vibrations through direct contact (think of a violin bridge). Both mechanisms contribute to the resultant sound, & transmit their sound augmentation through the heads (our speaker cones). Once you understand this, it's pretty easy to work out what constructional changes will do to the sound.
I was going to cut to the chase here, but I think it would be useful if I sight 2 extremes of construction to highlight the above;
1/ Ford drums produce a very thick shell ply drum series and coat those shells in a hard rubber based finish. They claim that the shell makes no contribution to the sound, & that their thick shell increases tuning range & produces a focussed tone. Applied to this specific construction, they're correct, but why? a/ the heavy ply construction is a poor conduit of vibrations from the batter bearing edge to the reso bearing edge. b/ the heavy shell isn't excited sympathetically by the sound pressure waves within the shell. c/ the coating adds further mass & introduces an element that resonates very little, & at a different frequency to the shell body.
Why they then fit suspension mounts is beyond me, but hey? A benign shell offers no significant tone shaping, therefore the sound is almost exclusively generated by the heads. The sound profile of the heads is therefore only shaped by interaction with the bearing edge, head selection, tuning, drum diameter, depth, & hoop mass choice. in other words, there is no sweet spot, so the drum performs in a uniform manner across the tuning range, & is limited only by the vibration/tension characteristics of the head material. This is a very valid all purpose gigging construction, and produces a generic drum tone.
2/ My prototype kit. Very thin stave shells. This is the polar opposite of the Ford design. The unmolested vertical grain structure of the shell efficiently transfers vibrations from the batter bearing edge to the reso head. The thin shell is easily excited sympathetically via the sound pressure waves in the drum. Every substantial resonating part of the construction is made from the same material. The shell is able to vibrate freely because there's nothing acting as a resonance sink by way of solid contact or differential mass. The result is a drum that opens up with the smallest input, & who's resultant tone is massively shaped by the timber species. This produces a very pure representation of the timber's tone. Such a construction is far less flexible than the Ford construction. It has a very defined sweet spot. It's peerless at doing what it does, but it's a specialist instrument.
Detail stuff;
Ok, background out of the way, Larry's first question related to purity of tone. With reference to the above examples, both produce a pure tone. The Ford produces a pure benign tone, & the Guru produces a pure timber species tone. You take your choice, both are valid approaches. In terms of the affect of lugs, & again, with reference to the first section of this post, their contribution is pretty much their mass, & the introduction of materials that resonate at a different frequency to the shell. In the Ford drums example, it really doesn't matter what lugs you bolt to the shell, in the Guru example, it's critical to the concept & outcome. Where I'm coming to here, is that the benefits of free floating constructions relate very much to the shell construction.
As Larry pointed out, all contact elements of a drum's construction vibrate, & therefore contribute to the sound. This also includes free floating mechanisms, but there's a caveat here. The contribution of the component to the resultant sound depends on how isolated it is from the primary resonating element. For example, the hoop is directly connected to the drum head, therefore it's influence on the vibration behaviour of the drum head is significant, but it's influence on the resonant behaviour of the shell is minimal. Lugs are directly connected to the shell, therefore their affect on the shell resonant behaviour is significant, but their affect on the vibration behaviour of the head is minimal. There's an umbrella element to this too, no matter how remote from source, the total mass of the drum construction will affect the overall character proportionally to it's size, so this is a complicated compound net affect.
Specific questions;
Don't the lugs, by virtue of being under tension and somewhat connected to the head, transfer a lot of energy to the shell, which then excites the shell more and add more of it's flavor to the mix?
Not really, the contribution is minimal, & also, undesirable, as any resonance has been coloured by the metal structures = additional overtones, usually high ones. The mass of the lugs detracts greatly from the shell's ability to resonate. On a thick & heavy shell, it's not an issue, but on a thinner shell that's advertised as being resonant, to add huge lug mass is just counter productive, unless you want a thumpy focussed sound.
Is it fair to say that a true free floating design has the least shell involvement?
Quite the reverse. If the free floating design is well isolated & of comparatively low overall mass, it delivers the most shell involvement, as the primary shell excitement mechanism is via direct contact through the bearing edges. Of course, the whole idea becomes pointless if the shell doesn't resonate freely. i.e. the more resonant the shell, the bigger the benefit, that's why free floating systems work best on thin solid shells, & especially steam bent, where some of the transfer is presented radially due to grain orientation.
For tone and character, the more shell involvement the better, right?
Absolutely, if that's what you're after.
Phew, that was a post marathon! Hope it actually gets read after taking forever to compose/type it.