nullcorp

You got a lot of long answers, but to distill it a bit further, you are DEFINITELY in 4H with your hand and slam is on the table. Most players would consider jumps over opponents as weak (i.e. 3♥) and the stronger bid here is a 3♦ cue bid showing support and limit raise +. The big difference is the former can be passed. Obviously the cue can't be unless your partner has lost their mind. I frequently tell students (I'm no expert btw but I teach beginners) to not mess around with other suits once a strain is identified. The longer answer is that you can make forcing bids (e.g. 2S, X) to get more description in certain cases. This isn't really such a case. My plan would be to bid 3♦ and see what partner does. 3♥ is minimum, 4♥ implies a bit more. Any non-heart bid (except NT) at this point is probably a control sequence, and 3NT would be semi-serious to play.

I agree as well, leading the lone Ace of your side's bid is usually okay. Particularly if you have a big fit, it's unlikely a guarded King (Kx, Kxx) is to your right. (If it's to your left, that's all you were ever getting, and you only do damage if your ace lead is trumped.)