This is why I like playing against regular partnerships, then can tell me their opening and raise style.
How about this for a train of inference:
Diamonds should be 6-3 from the auction and from LHO's lack of a raise to 4.
The play in clubs looks like they are 4-4, because LHO might have bid 3C looking at KQJ109x, and also the play of the 9 on the second round looks more like it is from KQ109 than from a solid suit (a restricted choice type argument if you like).
Therefore RHO is (21)64. RHO doesn't need either major suit queen for a 2D bid (if I ask about the point range I know I'll be told "no agreement"), but also could have either (or both) of them. That makes LHO favourite to hold both major suit queens. LhO would bid 3D with or without any of the queens, so I don't think I can tell much more from the auction.
However, if spades are 4-1 and RHO has singleton 4 or 3 then I have a spade loser anyway. So the first step is to cash the king of spades.
a) if RHO plays the 4 or 3 I assume spades are breaking, in which case RHO has a singleton heart so I cash the King and finesse.

if RHO plays the Queen I assume it is a singleton and cash the AK of hearts.
c) if RHO plays the 7 I think I going to play for it to be a doubleton which means finessing in hearts. With no inference from the choice of spade, the a priori odds just favour RHO to be 2164 and LHO to be 3334 rather than 1264 and 4234, if you decide they would both bid the same way.
d) If RHO plays the 9 I don't know. Does he look like the type to give count religiously at this point? As I'm playing LHO for the SQ, I think I play for it to be a singleton, so I play for the drop in hearts. When RHO turns out to have started with 97 and I congratulate him on the false card, it will turn out he's just giving count in the suit. Sigh.
S: 4H
Lead: DA