i knida like checking back, cause betting will induce a lot of choves and put us in a weird spot where we have to call, but are really never in great shape.  I think over-bet shoving is the worst option for the reasons you state, you are only getting called by hands that have you in somewhat bad shape.  Bet calling like coolers said is pretty solid, as he will jam KhQx KhJx etc….  It's a higher variance play, but I think it's way more +ev than open shoving.  If you check back, you can call lots of turns, and bluff lots of rivers when you miss, because it makes it look like AA, KK, QQ no hearts when you take the raise, check back, call turn, bet river when check to assuming the board texture doesn't change dramatically.  Obv. if hearts fall you're golden so I think that line is a pretty good alternative.  Idk i think it's close between that line and bet calling shoves/ bet jamming turns, i would only bet 3k on flop though, because it gives you much more FE on a turn shove.