[Chamonyx]

With that many players in the hand, your check/call plan on the flop is not too bad - someone is probably going to bet it for you, even though you have 3 hearts. Depending where the bet comes from and how many callers, you can also re-raise here. As you are last to act on the bet I would probably min re-raise here and expect at least 2 callers with 7:1 odds.

When the low card comes on the turn, I think here you have to pot it: Firstly you can't run the risk of everyone checking round for a cheap low draw. Secondly you don't want to let people have a free card for a boat. Thirdly and most importantly you want to build the pot so that if you end up splitting low after the river, your 3/4 is worth as much as possible.