If you play new suit forcing over a preempt just bid 3 spades and wait for partner's response. Then you can key-card (or other Blackwood form). I wouldn't have been worried about missing 7 because my partner(s) won't preempt with a side ace.
I agree with monikrazy. Partner didn't double so may not be short in hearts and your Q of hearts useless. If partner isn't short in hears, your Q of diamonds is also useless. So now you're looking at a 4-3-3-3 with a fitting Q and J in partners suits. Not much to recommend any kind of raise.