fine played postflop, don't think leading on the river make sense vs reggy opponent. You aren't have any bluffs with this line, so checking river seems solid (sets,flushes, top 2). However if this guy have sets/weird value or stationary, I believe we can forget everything and just donk shove.
Pre mostly squezzing, KQs playing well in sqz spot and we want to take it down pre.

Preflop - Both squeezing and calling is fine you close the action and it is not that much more to see a flop with a reasonable/good hand.
Flop - Yep check/calling mode want to keep all villain in the pot
Turn - Still check-calling can here as MP might come along although check raising to get more money from a set of a A high flush draw is another option.
River - Would lead out small as if it was a block bet with top pair or so against a made flush . Sets and good pairs will certainly call 1/3 pot bet. Same if river paired would still lead out small but now fold to a big re-raise.

Some sort of a $.60 or so blocker on the river seems good to me. Give you some maneuverability if you get jammed on. I doubt sets ship river and two pairs shipping river is even more of a stretch. Sets and good but vulnerable hands can potentially call river and I think it is far superior than checking in a spot where all two pair+ will happily check back when they would call a reasonable bet.