I agree with some of what you said. Hero's preflop range is definitely capped. I'm 3b most of my wheel suited ax, many of my suited connectors, 3b Ajo always, typically not flatting AA but sometimes flatting.
Co imo should almost always be betting this flop. His decision to xc is what makes the hand interesting imo. This board definitely favors his range and doesn't hit the Hero's or UTG1's range very often. UTG1 potentially could have a set of deuces (bad players still open limp bad pocket pairs in 2018), or an ax hand he may have open limped preflop, but is very wide. Some players are also open limping middling connected suited and offsuit hands like 89o and 10jo.
The co will have all the sets (except maybe not 22), a lot of Ax, some decent drawing hands like KQdd, KJdd, K10dd, QJdd, Q10dd, etc. Given our (Hero's) range is capped pre, I don't think there's too much merit to Xc. The hero will not have many value hands or strong draws, and likely will not be betting very often. Hero will have 22, sometimes 99, sometimes A9s (though this hand might sometimes be 3b), rarely AA, maybe some Kxdd, but KQdd and KJdd will be 3b a good amount, and Kxdd might just elect to check back the flop given the co's range advantage.
As played, I like a bet from Hero as our actual hand is strong and we want to charge some of our opponents' holdings, but again, this board does not hit much of the Hero's capped range, and thus this betting range is likely not very balanced. I actually question whether the co could exploitatively fold a lot of his weaker Ax hands on this flop because of that.
I agree that the turn rarely hits the Hero's range (in fact what hands could the hero even have here that improve on this turn?) While the turn favors the co's actual hand by giving him a nfd, this card also doesn't improve many of the hands in the co's range. The co at this point probably has mostly middling Ax, a set of aces, maybe some flush draws, maybe a set of nines. I'm not sure what hand the co might donk with, other than maybe a set of jacks, as JJ could potentially xc on the flop. This does not seem advisable, however, given the J so rarely hits the co's range.
I agree the Hero should continue betting here on the turn. Given the co's hand, I think xc makes sense. Xr seems bad because it would not be a good spot to have to stack off with just an Ace and a flush draw given we are relatively deep, and the co would not want to get blown off of his equity. We also established that when the Hero bets flop, he is likely unbalanced.
Additionally, I think we can rule a lot of hands out of the co's range at this point. He will rarely have KXdd, as those hands would usually bet on the flop. A9s likely bets on the flop as well. AJhh is a possible candidate for value (though this hand likely bets the flop too), in addition to JJ.
One of the main questions I have is what hands make sense for the co to donk here? I agree A7hh seems like an awful hand to donk with. A7hh plays much better as a bluff catcher and could potentially win at showdown. Additionally, while hearts are probably less relevant, his hand blocks something like Axhh that the Hero could have flatted pre and double barreled (though a middling Axhh might check back the turn). Further, a lot of the villain's stronger flushes likely would have bet the flop.
JJ and AA are very unlikely to xc flop xc turn. To that end, is the villain even repping anything credible? Or did he just burn $412.50 betting a hand that rarely gets called by worse, but has some merit as a bluff catcher, has poor removal (except blocks AA), and potentially has some showdown value?