Well that all depends on your opponent and what we think his level of thinking is like. If he's thinking about what we might have and has a semi-decent understanding of bet sizing we should bet smaller imo since it then LOOKS like thin value without really being thin value. Or if we think he is prone to hero calling we can even overbet ~$3.20 or something to get max value out of his hero calls. Since we're fairly sure we're ahead here we're just trying to figure out exactly how much value we can get from him
I don't think betting 2/3 to 3/4 pot would make it look more bluffy as to me that just looks exactly like what it is, you caught a K on the river after betting the flop with overcards, perfectly reasonable. But again we come back to the opponents tendencies? Is he thinking about what our bets might mean or is he just looking at his hand and betting/checking/calling based on the absolute strength of it? Since we have him noted as a Good TAG then i'd guess he is at least attempting hand reading so I don't think betting 2/3 - 3/4 would make it look more bluffy to him. If we were against a calling station fish then we can consider just potting it and hoping he calls with a random 2nd or 3rd pair.
Regarding cbetting here with AK, I would almost always bet here on the flop with AK. Whilst your thinking is correct (Congrats on that btw) that no worse calls and no better folds since there are so little draws, when we cbet with AK here we bet to pick up the dead money in the pot and fold out his equity share, which is quite large due to us not having a pair here (He has at the very least 6 outs to beat us).
So I like your thought process regarding betting AK, but the problem is we can't really face a bet if we don't hit, so if we check back the flop and villain throws out a mandatory bet on the turn which he can do with any two cards then what do we do? Yeah we can definitely call one street, but by the river our range is extremely polarised (Flopped set or A high/2nd pair) which means villain can then bet/fold any river, and we really can't face a river bet with A high here when his range could have literally anything in it