when I have 12 cards in 2 suits I feel very comfortable forcing us to the 4 level and Michaels shows 5 cards in the other major plus a 5 or card minor. I am sure pard would bid 2nt over 2h with qx xxxx xxxx xxx Partners shape rather ...
I cant imagine not just biding a simple 1h or whatever bid you make in you system to show hs. They don't have to have 4 h when they make a takeout double and u will never find your h fit if u start with a p or 1nt.