un6c

It's a tough call. Game-forcing hands with 3-card support for partner's response are just hard to bid, in particular in standard-ish mehods. There are nice treatments available, including artificial meanings for jumpshifts/reverses, or Gazilli in this auction. But in a pickup partnership, you are stuck. With the kind of pickup partner you seemed to be having, I am not sure a jumpshift into a 2-card suit would work out that well. Obviously, 3H and 3S are out, being non-forcing. So in my opinion, it comes down to 4H or 4S. Between them, I kind of prefer 4S - seems more likely to work out. Moysian fits are not the end of the world, in particular if you have shortness with the short trumps.

As awm's partner in the event where this hand occurred, let me add one point that no one has touched upon so far. Those of you who are saying you would pull to 3NT did not comment on the second part of the question "Do you agree with the auction so far?" I think this is really the key: If you are going to pull to 3NT after partner doubles 2♠, why did you pass 2♠ in the first place? Did you learn anything from partner's X of 2♠? Would any action by partner (except an impossible pass) prompt you to not reach an eventual contract of 3NT?