Coups are Sexier than 3-3 Splits

Here was an interesting declarer problem I faced on the last board of the session last night. It's one any novice would get right because they would just draw 3 rounds of trumps early and be home free with the round kings both onside. However, I had a chance to play for a trump coup instead of a 3-3 break. Here is the deal, with hands rotated for convenience.

Dealer: S Vul: Both	North ♠ AK ♥ AQxxxx ♦ KT ♣ Qxx
	South ♠ Q98xx ♥ x ♦ 97xx ♣ Axx

South	West	North	East
Pass	1♦	X	Pass
2♠	Pass	3♥	Pass
3♠	Pass	4♠	Pass
Pass	Pass

The defense started with A and another diamond, east echoing high-low (standard). Things look bleak. Setting up hearts is pointless because you'll never be able to get back to them after trumps are in. Trumping diamonds in dummy is no good because the AK are really needed to draw trumps. So, I played the ♠AK. West played the T on the second round. I next played a club to my ace, and then took the heart finesse and cashed the ♥A, and led another heart, pitching 2 diamonds. West then cashed the ♣K and led the DQ. After trumping this, I am left with ♠Q9 ♣x and the good ♣Q in dummy. West started with at least ♠Tx ♥KJx ♦AQJxx ♣Kx. If his 13th card is the ♠J, I need to play the ♠Q now but if his 13th card is a club, I need to play a club to dummy so I can score the last two tricks with ♠Q9 over east's ♠J8.

A priori, it is more likely that west started with 3 clubs and 2 spades than 2 clubs and 3 spades because there are more outstanding clubs than spades.
Should I take any inference from the fact that west cashed the K or not? If the defender is actually thinking about the hand and counting it out, yes. Against these defenders, probably not - they probably just thought I might pitch away the rest of my clubs on dummy's hearts. Anyway, it's pretty much a double-dummy hand for the defense. If he taps me in diamonds when I let him in with a heart, he can tap me again when in with the ♣K, thereby forcing me to play for a 3-3 spade split. (If I started with 6 spades, it matters not what the defense does and if my spades are any worse than Qxxxx, I'm always going down so this is the only relevant spade holding). Therefore, the choice not to tap me by playing a high diamond should indicate that spades are 3-3 and he wants to present me with the losing option of a trump coup.