You should not stop short of game. It might go down, especially if the
♠A is missing and led followed by another trump, but it's worth the try.
A possible reason to bid 3
♠ is, that you hope to bid 4
♠ over 4
♥ and make them Oppos think, that they pushed you into an infeasible game and let you play there. However, looking at
♥AQxx they're not going to bid 4
♥ very often... I know someone in my club, against whom I might take that approach.
I'm not entirely sure how much I want to involve partner in a possible 5lvl-decision. It's quite unlikely that either opponent bids 5
♥ in the first place and secondly the wasted
♥Q severly lowers my ODR. I have 5
♥ beat in my own hand and partner needs perfect cards for only bidding 2
♠ and 5
♠ being on. Something like KJxx,x,Kxxx,xxxx is no 2
♠-bid for most and if he has that 5
♥ is going to be painful
If the
♥Q were a small
♥ and in return a small
♠ the
♠K, I would strongly consider bidding 4
♣, because now 5
♥ will not nearly be as painful and partner is much more likely to only bid 2
♠ with 5
♠ being on anyway, if he has no
♣-wastage