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I'm a little suprised that everybody is against the preflop three bet. Yes, it is a bit unorthadox, but we're not required to play from a book, and believe it or not, it isn't much of a mistake if at all to do so here.
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Depending on the limit, most unknowns don't raise preflop enough, meaning 77 is a dog against their range. People's UTG raising standards are usually tighter still; I read a thread once where Schneids posited that it's about half their overall PFR%. Taking both of these into account 3-betting 77 can be pretty bad.
Remember the gap concept: you don't want to get into a hand with a holding that is only a coinflip against the PFR's range. You're getting only slightly better than 1:1 on your money by 3-betting and I don't see a significant expectation of making money postflop. In fact, I think you're more likely to lose money as villain will release his unimproved high card hards, but you're inclined to go to showdown in case he continues with them.
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In some situations it would be correct to call the turn and fold the river. Yes, that sounds somewhat strange, but against certain players you can almost always fold this river. Even if you couldn't, you could still call down, which isn't significantly worse (if at all) then the free showdown play.
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I like your argument against the free showdown play, but I don't think folding the river is correct here. Decide on the flop whether or not to take this to showdown. If you decide to take it to showdown then call a river bet, because many players will bet AK one last time for value. They might be hoping to fold another AK, but folding your 77 is a coup.
The main problem I have with your arguments is that they necessitate a particular sort of opponent and are plays that should only be made with a specific read. This villain is unknown, and while he might fit the criteria chances are he doesn't and there's no way of knowing without playing more hands with him.