1D promised an unbalanced hand, either a 6 card suit (can be 6322) or 5422 or more unbalanced and can be 4 cards only if 1444/4144/4441 or 1345/3145 weak clubs, strong diamonds.partner will open all 11 counts.
2H was a weak jump overcall. Your 3C was essentially game forcing, although in theory one could stop in 4C.
The double of 4H simply said he didn’t like his hand for clubs (and wasn’t stiff or void in hearts). It wasn’t ‘penalty’ as such but there’s some expectation I may pass unless I have a reason to bid.
Well, you definitely appear to have a reason to bid.
You’re playing imps with and against experts.
Your call, and why?
++++++++++++
Hard problem with scope for confusion. In such high-level competitive contexts, DAvid Kok is right that we should try to agree general principles. e.g.
5N = pick a slam.
4N = 2 places to play. often minor orientated.
Major cue = suggests/other major.
Any agreement is better than none.
Handicapped by a dearth of such understandings, I rank...
1. 6♣. Paul's practical pursuit of the plus score.
2. 5♠ Paul's alternative: an unambiguous black 2 suiter suggestion.
3. 5♥ to suggest ♠ but partner might not judge ♠Qxx to be adequate support.
4. 4N might be OK if you can persuade partner that your other suit is ♠.
4. 5N to suggest 2 places to play. Correct the likely 6♦ to 6♠, but 6♠ might be too high.
5. 6♥ a good hand but woolly and optimistic.