Reno Jacoby Swiss

Here's a hand from the last match of the Jacoby Swiss when we and our opponents were already assured of playing in a different event the following day (spots approximate).

North: ♠AK8532 ♥J832 ♦– ♣Q93
South: ♠764 ♥AQ65 ♦862 ♣AK7

Auction:

North East South West
 1♠    3♦    X    4♦
 4♥     p   4♠   all pass

With 2-2 trumps, the ♥K onside and doubleton, thirteen tricks were there.  The opposing team got to a small slam (at the other table, East bid only 2♦ and West 3♦).  How should we have reached 6♥ or 6♠ if at all? Comments welcome.