i think leading is better than check raising here since the CR gets us into a bad spot a lot of the time on the turn

many thinkers will call the CR putting you on a monster/draw and look to get it in on a non-heart, non A turn.

by leading we have a better chance of getting it in the flop and we can avoid never getting priced in as a relatively big dog on the turn

also when you bet flop and miss the turn a fun line is to check turn and check-raise every river if villain checks behind on turn