Is it crazy to think the flop is actually close between call/fold with our really weak back-up? I still think it's a call with 6-out redraw to the nuts, especially if CO potting with naked JT often... Definitely not a great spot though as our equity multiway is pretty low if one person has a set and the other has JT+any hearts, per the output below. That would be like absolute worst-case scenario so in reality you're probably much better than 20%, but not a thrilling spot
Jamming turn for value makes some sense, but at these stack sizes, CO can't really price out BTN. If you pot turn $800 ($200 behind) and CO jams for $2000 then BTN has to call $2000 to win a $3800 main pot + $2000 side-pot... the equity math is not so straightforward for BTN because of the main/side pot but he still has odds to call with something like QQ+gutshot or something. So I don't think CO can really force him to fold, but it's still a better line than check/jamming since you get BTN's extra $1000 in the middle with his draws, whereas he might just call the $1000 jam and fold rivers when he misses, saving $1000