Late to the thread, but here are my thoughts fwiw:
1. I would always respond 1H to 1C, even if playing that 1C showed 3+ (I happen to play transfer walsh in my two current serious partnerships, and 1C could be on 2).
There are at least two reasons for this. Btw, I don't 'promise 5-6 hcp' for this bid, and few NA experts would, either.
a. Partner will be making any number of rebids, but most of them will leave me better positioned than passing 1C. He may bid notrump, and I will go back to hearts. Now, I hope that over 2N I can get out in 3H (there are at least two decent methods that allow that, Wolff signoff or transfers). But even if we are compelled to 4H, it may have a play and may be better than 1C anyway. He may raise hearts! He may bid spades: I have an easy pass of 1S, for example. Of course, some rebids, in clubs, are going to make me wish I had passed. On balance, however, my experience is that we will more often improve the contract by bidding than by passing
b. We pass and the opps may have an easy 'penalty' pass, but this is linked to point 1. However, the other aspect of bidding over passing is that LHO may be unable or unwilling to bid over our unlimited 1H call, and so we may be able to jam the auction merely by suggesting values and taking away at least a modicum of bidding space.
Having ventured 1H, partner bids 2S. Forcing. And we have all been trained that passing a forcing bid is a mortal sin.
Rules are guidelines. Passing a forcing bid is not something to be done more than a handful of times in a bridge lifetime, but bidding here is ignoring the object of the game: to maximize our score.
We can be fairly confident that 2S will make. We can be almost as confident that 4S won't (though it is far from impossible).
Were we playing imps, I would bid: what I would bid would depend on agreements. I like 2N here as ambiguous, with 2N then 3S being the weakest holding I could have, but that may not be available. I think 3S should be more encouraging than 4S, but I'd like to know something about partner's experience, and tendencies before making my call. At imps, passing and finding partner with, say, AKQ109 x x AKxxxx, which is borderline for 2S in terms of hcp (but not playing strength), would be too depressing. At mps, however, we are concerned with frequency of gain, not size of gain, and the smart money says that 4S will usually be too high.
Obviously one needs a tolerant partner. The better the player, the more likely it is that passing would be understood, even if it led to a missed game. Experts understand that rules are guidelines, and one of the traits that make a player an expert is good judgement, including when to choose to break a 'rule'.
I see some comments suggesting weak jump shifts as the answer.
I don't play weak jump shifts. I have played them often, and still play them with the occasional non-expert partner, when he or she prefers, but I find them to be suboptimal. Right now, I prefer 1m 2H to be a balanced invite in notrump. One needs reasonable follow-ups but it is a powerful method. I have previously used it as meckwell (currently 1C 2D is meckwell, but we don't have gadget over 1D).
Bridge is fascinating in part because people tend to have strong opinions even when, viewed objectively, the situation is far more nuanced than the opinion-holder appears to recognize. This thread is an excellent example of that, including some of the comments.
For example, using this thread to criticize 2/1 is, imo, too simplistic. Yes, 2/1 has a fundamental flaw in that the 1 level suit openings are very wide range, and it often takes 2 or more rounds of bidding for the hands to be more narrowly defined. However, the popular alternative big club methods have different but, imo, equally problematic flaws. Without discussing 1D openings (because different pairs play different length agreements), the 2C opening is theoretically unsound, and the 1C opening is, admittedly infrequently, far more prone to successful preemption than is a 2/1 2C opening (because the low end of the 1C is so much lower than the low end of 2C, meaning that it is more difficult/dangerous for the 1C opener to compete after preemption than for the 2C opener. In addition, on many 2/1 hands, opener has bid a suit before the preemption, so fits may already be found).
All methods involve compromise. Imo, a fairly simple 2/1 method is more effective than a correspondingly simple 1C method. A powerful 1C method is probably better than a correspondingly good 2/1 method. In this forum, the 2/1 method is probably superior. I used to play two different big club methods, and so my views on this are based not only on observation but also experience.
Finally, I see cyber suggests playing 1S as forcing. I think it makes almost no sense to do so. When, if 1S is forcing, is opener ever going to limit his hand? I have known several non-experts play 1S as forcing. I have never seen a NA expert do so. Of course, low-frequency issues like this tend to persist because the sequence arises infrequently, and opener rarely has the big hand and, when he does, the partnership usually stumbles into the right spot anyway. Which is one reason bridge is so fascinating. No matter how silly our methods may be, we get enough good results, and tend to ignore the bad ones, that we can tell ourselves that our methods are good.
I do realize that all of this applies to me as well
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari