I think the initial action is close between double (intending to show clubs next) and just overcalling 2C. Obviously you are at the top of your range for an overcall, but (as you found out) SOMEONE has hearts, and it isn't you. Your LHO is quite likely to have some, and if he has a few points as well overcalling 2C makes it far harder for him to show them than doubling does. As the auction went he's probably too weak, but I think I'd have just overcalled 2C anyway.
After double, as the auction progresses 2C is clear. 3C is an overbid by approximately a king or so. You are minimum for a double-then-bid-suit sequence. 3C is the type of bid someone who thinks they have a really big hand will make, while not listening to partner put on the brakes.
As bid, after 3D, then I'd clearly bid 3NT. Partner's asking us to further describe our hand, and we certainly aren't going to show our heart support now
. And we've already shown our club suit pretty well. Time to show the diamond stoppers. Note that we aren't TOO afraid of hearts as partner has bid them, but then again we MADE partner bid something, so we could well get hearts jammed down our throats. 4NT is the type of bid that someone who thinks they have a really big hand will make, while not listening to partner try to put on the brakes. (Sense a pattern here?
)
Mike Lawrence explains the principle of putting one's hand in a "box" quite well. Here, after double and then jumping in clubs, you have described a HUGE hand with a club suit.
In the context of that, our hand is terrible. We have no heart fit for partner, our hand isn't exactly as strong as we advertised, and we have adequately shown our club suit. It's time to start to slow down the auction--if we have slam, partner knows what we have much better than we know what partner has. Partner's hand is in the context of "minimum response to takeout double" followed by "random forcing noise after partner shows a HUGE hand". We don't know what he might have, except that he probably has about 0-7 points and a few hearts. Let him make the decision.
Blackwood is a really really bad call here for a number of reasons. First, you don't know if you have a slam (my money is on no). Second, if you do have a slam, you don't know where to play it. Third, partner showing you zero or one aces really doesn't help you decide if you have a slam or not. Partner could have:
Qxxx
Jxxxx
x
Jxx
pretty easily here, no? That has a lot of play for slam--but you have no way of knowing it, and after Blackwood partner has no way of telling you.