Nice one for the defense

Friday we encountered a nice hand, but opponents fell asleep. Put yourself in their shoes.

You hold:
♠ Kxxxx
♥ Kx
♦ Jxx
♣ xxx

Everyone Vulnerable, your partner opens 1♣, RHO (= me) intervenes 1NT, and everyone passes.

What do you lead?

The player at the table started with a low ♠ which worked out the best possible way, but they didn't realise it. In dummy you get:
♠ Txx
♥ Q9xx
♦ Q9xx
♣ Tx

Partner takes ♠A, continues with the ♠Q and a small ♠ to your K. Declarer discards ♥T. You continue with 2 more ♠s. Partner asks for a ♣ switch (playing Odd/Even signals, he plays ♣5 and discards ♦T), while declarer throws away a ♦ and a ♥ from dummy while discarding a ♣ and a small ♥ from his hand.

Your turn again: what do you play?

At the table, a ♣ was played and I claimed 7 tricks.

Here's the full deal:

Dealer: East Vul: Both Scoring: MP	♠ Txx ♥ Q9xx ♦ Q9xx ♣ Tx
♠ Kxxxx ♥ Kx ♦ Jxx ♣ xxx		♠ AQx ♥ Jxxx ♦ T ♣ AQxxx
	♠ Jx ♥ ATx ♦ AK8xx ♣ KJx

I got triple squeezed on the 5th ♠, so I had to bare my ♥A (baring ♣K would be a disaster, and discarding a ♦ is throwing my 7th trick away).

How could West know what to do? Well, it's pretty simple imo. I don't discard any ♦ in my hand, so I must have 5 of them. With 4 I would keep them in dummy and discard one from my hand. I showed 2 ♠s, I must have 3-4♥s and 2-3♣s. Either I have ♣Ax and ♥ATxx, or ♣Kxx and ♥ATx. Looking at my discarding, I think it's clear that I only have 3 ♥s (the unblocking T at first opportunity), a 5332 is more likely to overcall 1NT rather than a 5422 with a good 5 card suit, so the best chance for defeating the contract should be to play a low ♥ from Kx and hope your partner has ♣A. Another clue that might strengthen this idea is that partner would probably act with a good 6 card ♣ (AQJ9xx or KQJ9xx is good enough to either double or rebid the suit), so he'll only have 5 of them.