I dont think I would call such a big bet (10% of my stack) heads up to set mine here against a good player who is likely raising with a hand better than yours in the SB. Especially if this good player is good enough to lay down AA or KK post flop. If its some loose rec player who can never fold AA… then maybe. But just based on odds to hit your set plus the likeliness that you get paid off with an entire stack later (by a good player) just seems unlikely. at best you’re a coin flip, but its likely pair over pair, and you either have to set, or bluff later to win. and pray its not set over set. 44 is too small in this spot for me.
That being said I think the river call is borderline at best, because the straight gets there. There is some of his range that you can beat. JTc is the basement of his range here, but AK/AQ clubs makes perfect sense. I dont think most people fire out 3 times here with that connected of a board (especially the jam on the river) with 88-jj type hands. Really, when you call the river you hope he has AA or KK and played it way too aggressively. But these are the ONLY hands you can beat here. The other option is he hit his set, but then youre dead cause the board paired. So when you called what did you put him on?