Well I am impressed, and mind-opened. You make some very good arguments for lighter gauge strings. Regarding the fundamental bit, I am wondering now if that is why Jeff Beck and Steve Vai and so many other cats who do lots of harmonics and squeals prefer lighter strings (whether they know it or not, it sounds like they get more overtones and harmonics from those thinner strings). Very interesting.
Go science, right? I am not saying light strings are best, I am just saying that they are not inherently weaker in the sustain department and that good tone is subjective and really more of a cultural construct (though I have considered a physiological theory as well, but psychoacoustics is a slippery slope). I think you are correct about Beck and Vai viz-a-viz light gauge strings. Also keep in mind they are both wang bar masters (abusers???). This will be more true of Beckola than Vai because the big V favors the Floyd rose system with all that locking hardware, but lighter strings tend to be easier to set up vibrato systems for. With less tension to balance with the springs its just easier to get your vibrato set up to be very responsive and to generally return to pitch when used correctly.
So basically I agree with you, there are so many factors... the wood type, the fretboard type (ebony bounces notes off the fingerboard more than rosewood, for example) and of course the string gauge. Heavier strings does not guarantee more sustain or better tone. But maybe, perhaps, it can help lean you in that direction.
but then there's the South American rosewoods like Kingwood and the now-elusive Brazilian variety... so dense and reflective. My older rosewood boards are very dense and bright sounding like my ebony equipped les paul, whereas unplugged my tele and modern SG have more in common with eachother tonally than the SG does with my older set necks or the aforementioned LP. Of course, they also aren't maple capped. So many things. Its best just to own a fleet of guitars and enjoy them for what they are, isn't it?
Anyway, the heavy-string sustain you are experiencing is probably a sense that the fundamental sustains longer with 10+ gauges while the harmonics decay quickly after the initial attack. So in a sense they are helping you in that direction by taking a guitar that is already well-designed to sustain with any type of string and allowing it to create the sort of sustain that pleases your ear. Picking a string gauge on these criteria is also like the decision to play on pure nickel, nickel wound or all steel wrapped strings.