Is there a set of fluorocarbons that have the punch and fullness of Nylgut?
Would it be worth it to try a different gauge of Aquilas?
Or would a different material (nylon, nyltech, gut) have the sound I'm looking for (punch, warmth & fullness with complexity & clarity)?
...am I looking for an impossible-to-find holy grail?
No to the first question.
Definitely yes on the second question. While the instruments' construction can often be the reason for a boomy sound, a loose tension on the C string will accentuate that note - give it more vibrato, and can also be a cause of a wolf note. Unlike some companies which simply use the same gauge string for every size ukulele, Aquila gauges are different between the Concert & Soprano size. It would definitely be worth your while to give the Concert set a try.
It's a bit difficult to answer the third exactly, as flourocarbon comes in various "flavors" when it comes to tone, and whatever density it is, it's characterstics as far as balance from one string to the next are very different from nylgut. Instead of going further into that, let me just say that there are a couple of nylon sets that would be worth a look.
Nylon now has so many varieties, and can be so far from the original Dupont formula that it's impossible to generalize about it at all. Some of the brighter formulations, however, have a balance and tone that I'd say fall roughly between most flouros & nylgut.
A lot of members here are familiar with the D'Addario Titanium strings. That would be one possibility. Hannabach Flamencos would be another. These sets aren't clear, but have semi-transparent colors - the Titaniums are a light purpulish grey and the Flamencos are a light copperish red.
I'd be remiss if I didn't mention ours as well. Our sets are made of mixed materials. It's a
lot more work to put together sets this way than just selecting a single material, and then gauges. We often have 4 different materials in a 4-string set. The goal, which I think we acheive pretty well, is to get better balance in diameter (more comfortable playing), tension (ditto), and most importantly, tone. We avoid to a large extent, one of the main problems of sets from a single material: the thin strings being overly bright, or the thick strings lacking clarity.