When kings are like aces

This hand is from online bridge with IMP-style scoring. I didn't play it, but xwing showed it to me and I gave it to two friends to bid. Suppose you hold this hand:
♠ K 10 ♥Q 7 6 5 2 ♦Q 8 5 ♣ K J 5.

Partner bids 1♣ and you respond 1♥. Partner jumpshifts to 2♠. What now?

You "mark time" by bidding 3♣ and partner jumps again, this time to 4♥. You and partner have discussed this. He has a hand that is too strong for a 4♦ splinter bid over 1♥. Therefore, he made a jumpshift and jumped again. If he had bid only 3♥ over your 3♣ call, that would show a strong hand, but only three-card heart support. Bidding 4♥ confirms four-card heart support. This is the old-fashioned way that players had to bid before splinter bids were invented.

Now what? Your hand has grown up. You have a fifth heart, and your two black kings are like aces. You try 4♠ and partner jumps to 6♥, ending the auction.

Here are all four hands (rotated for your convenience):

                  ♠ A Q 7 3
                  ♥ A K 8 3
                  ♦ ---
                  ♣ A 10 8 7 6
♠ 8 6 5 4                    ♠ J 9 2
♥ 10 9 4                     ♥ J
♦ A K 6 3 2                  ♦ J 10 9 7 4
♣ 9                          ♣ Q 4 3 2
                 ♠ K 10
                 ♥ Q 7 6 5 2
                 ♦ Q 8 5
                 ♣ K J 5

How do you like your contract? If hearts divide 2-2, and nothing else
splits poorly, you are odds-on to make seven. Draw trumps, play three rounds of spades discarding a club. Now play ♣K A and ruff a club. If the suit sets up, you have 13 tricks. Because things don't split very well, the small slam is high enough.

Thirteen out of 54 pairs bid and made 6♥. Some had effective big club auctions. In some cases, West opened 2♦, North doubled and South jumped in hearts. This was all the encouragement North needed, so the preempt worked against West. A few of the 13 just guessed.

You can see what everyone did if you click here.