Beyond rules of thumb

Playing in the club qualifiers for the Grand National Teams, we were playing an A-flight team.  It was in the middle of the event, and we were still in it.  I didn't know it yet, but our team would finish just 4 victory points shy of first place. If only I gotten this board, right ...

What's this board that I wish I would have gotten right?

W

Pard

♠

Jxx

♥

Jxxx

♦

10xx

♣

xxx

Lead: ♥K

E

Me

♠

AKQxx

♥

—

♦

AKJxxx

♣

Jx

I was in 5D after this auction:

W

Pard

N

RHO

E

Me

S

LHO

—

1♣

Dbl

1♥

Pass

2♥

3♦

4♥

Pass

Pass

4♠

Pass

5♦

All Pass

I ruffed the King of hearts that was led and played the Ace of diamonds.  LHO followed with the 7 of diamonds and RHO with the 3.  Decision time.

I had two options:

1. Play a spade to the Jack and finesse the Jack of diamonds.
2. Bang down the King of diamonds.

What would you have done?

At the table, I woodenly followed the "eight-ever, nine-never" axiom and banged down the King of diamonds.  LHO showed out, and 5D was down one.  At the other table, they were in 4S after our teammates playing Precision opened 1D (11-15, 2+ diamonds) and the person in my seat doubled and bid 2S over 2H because he was not sure what a diamond bid would mean.

I could have done better than the apriori odds. I have 18 high-card points and partner has 2.  Assume that opener has 13 and responder 7.  Why would responder with such a weak holding go all the way to 4H after my 3D bid?  The only possible reason is that LHO has a distributional hand, with a double-fit and shortness in my suit.   LHO is likely to be 6-4 in hearts and clubs (of course this means that RHO raised with 3, but holding AJx, he probably would).  Also, since there are 5 spades and 4 diamonds out, her singleton is most likely to be diamonds.  Everything fits the 2-6-1-4 theory. I should have taken the finesse.