Raise flop. This guy's never gonna put anymore money into the pot with AK AA KQ without a flush on heart turns and rivers, but his range on the flop is super strong and probably contains close to no air, so we're getting lots of money in miles ahead here by raising and folding out nothing but the hands he'll shutdown with anyways. He also likely stacks off with hands like AhQx and AhJx right now but not on blank turns and rivers. Leaving CO to take a cheap card here is fine on dry boards but on this texture we just need to be raising now while he also stacks off with all his Kx which we obliterate and also his dumb ass pair + heart hands which often a tard like him wont be able to fold even to a line this strong. We don't want these hands taking a cheap card and would much rather make him make a big mistake by putting loads of money in with 25% equity rather than play well vs us by calling with a good price to improve then fold rivers unimproved.

Basically, we're miles ahead on the flop, and can get ass loads of value there and then from various hands we crush, but can't get this value on a lot of turn and river cards.

A few comments on your ranges for SB. This preflop range is too wide, while a guy like this will play mainly PPs facing a raise, he'll be happy to complete most of them in a limped pot and will only raise good ones and good broadways. Something like 99+ AJ+ is likely more accurate.

Your flop range is really good, obv 44 is less likely due to the above, but besides that spot on.

At the end of your post you account for the fact that stacks go in on non h rivers, and we don't want them to on h rivers anyways. This is correct, but remember that the reason we don't want them to on h rivers is he now folds a ton of hands he stacks off with on the flop/turn that we can get him to put his monies in with on those streets! There are 8 combos of AK and 3 of AA that don't contain hearts get their monies! There are 8 combos of Ahx hands with no pair, get their monies, you crush them!