How to bid best?

Some may find this easy, maybe even trivial to bid. But this is the bidding from todays expert. He obviously downgraded the South hand. 1NT is alerted as 7-11 points. But even if he had bid 2NT, the problems persist. It is not easy to select between 3NT, 3♥ and 4♥ for North. The best contract is 3NT, by the way. 

I reached 4♥ like some other players which make with good luck. I play 2/1 with Lia who opened his 5-card suit. My response was 2♦, alerted as forcing by Lia's system. To the partner this looks like heart shortage and an own suit. The rebid was 2♠. This cuebid is alerted as "default bid, forcing". Then I went for 2NT, downgrading the hand. But that was not stopping North to repeat the cuebid, probably asking for a stopper and forcing to game. I reached the  optimal contract. But North understandably fixed to 4♥. 

This hand is a perfect example of the judgement problems you face in Bridge. I have no proper solution. Clearly, partnership understanding helps. In retrospect, I believe that 2NT is the correct response, and that it should show a balanced hand with a spade stopper and 11-12 points. North does not know about the diamond stopper then, and he wants to play in hearts anyway. But he could try 3 showing his stopper there and South might offer 3NT.