🚀 go-pugleaf

Holding KT84-3-AQ82-KQJ the bidding goes 4H-4S-7H-?. What do you do?    
Vul vs NVul. a)imps  b)matchpoints
  
First I'll assume the solution has nothing to do with calling a miss-deal
for holding only 12 cards, so I'll pretend I have another low card somewhere.
It makes little difference on the analysis which suit it is.
  
I've always disliked bidding problems. Probably because my partner always 
misinterprets my bids! Never mind that partner claims that I consistantly
make the wrong bids and convey the wrong information. Usually there are
a multitude of bids available and I get terribly confused. This time
even I can narrow the choices down to three which gives me a 33% chance of
guessing right. So I've gathered up my courage to speak up and give my
one cents worth.
  
Double seems obvious. How can my opponents possibly make their contract with
all my high cards? Its best I tell my partner this information right away.
But wait, didnt I just read something about a new convention? I didnt pay too
much attention because it seemed silly to bid a lot higher than what you
could possibly make. Probably doubled on top of it! Why would anyone want
to voluntarily give the opponents points? They called them preempts or
something. And my partner did make a bid on the 4 level vulnerable so he
must have a good hand. What are the opponents bidding on? I better bid 7S
to tell my partner I have a good hand too. But wait, what if we have a heart
loser? Partner will surely be upset with me. Why should we give the opponents
points after their outrageous bidding. Maybe I should double after all telling
my partner I dont think 7S can be made. Suddenly I've become terribly confused
once again. So, like always, after 32.5 seconds of mixed up thoughts, I meekly
make the following bid: "pass?" After all, how can I possibly convey the wrong
information with a pass. My partner should know by now that a pass by me means
I dont know what to do. Yes, partner will be very pleased with me this time!
He now has enough information to make the correct decision.
  
For the record, normally if the opponents sack at the 7 level over your six
level contract, a double denies control of their suit and a pass implies a 
void. But this is usually only after you have previously described your hand
and have signed off in the final contract. This time you haven't. Can partner
infer that your hand is good enough to bid 6S without competition? If so,
does the above situation apply? Maybe, but then again maybe not. Who knows?
Anyway, I personally would take the following view. In imps, I would double
for the following two reasons:
   1) tell partner I dont have heart control and to be careful because...
   2) the opponents should not bid 7H pushing us to 7S if they think we can
      make it. They should try to get the bidding passed out at 6S, so I
      would expect a bid of 6H if they had nothing.
  PS) by the way, I would pass with a heart void and never commit the hand to 7SIn matchpoints, I would pass for three reasons:
   1) Partner knows that with heart control and a reasonable hand I'd bid 7S
      because it pays to bid aggressively
   2) the opponents most likely have a total bust because they feel 6S is cold.
      If they had an outside ace they most likely will try to set 6S and only
      sack up to 6H. Why go for -700 when everyone else is -650 or +100.
   3) tell partner I have interest in 7S. A double would deny any interest
      at all. I would expect partner to bid 7S with heart control.
  
post-mortem: I've probably lost another partner.