Why would you shove 350 BB into a 18 BB pot with QQ after V limp re-raises? AK has the benefit of card removal blocking AA and KK cutting those 12 combos into 6. QQ doesn't really block anything useful. I think your play is more long term losing than V. V can easily fold all of his weaker
hands and bluffs to your jam and call in position with KK+, AK. Which has your specific hand beat 60/40. If he can see your hand then sure he's a slight dog and should be folding to such a large bet but it's not a crazy call if he thinks you can have AK and QQ in your range (which you probably do). Are you making the same jam with KK or AA? I doubt it.
I'd recommend 4 betting to 30 BB since we are OOP and playing poker. You haven't given any reads but based on the player we can still then fold to the 5 bet or call it off or jam over top based on the player. If we make it to a flop and there's no Ace or K we are much less likely to get it in bad. As played we got called by probably the worst hand he has in his range and we are still only ahead 57/43. Many times we'll be in much worse shape than that.
