Sorry to hear you are going through this mess...PLEASE try to stay calm and colleceted when communicating about such sensitive issues. I can see your emotions seeping into your communciations to H.
Here's what I would suggest;
H,
While it is true we may each wish to share our relationships with S, I feel that we should come to a concensus regarding when that might be appropriate. It is unfair and unreasonable for us to introduce S to someone, allow him to get attached, only for another relationship to end and him to be hurt and confused again. I feel that we should try and insulate him as best as possible from this at this time - he has enough to deal with and really does not need to have more to think/worry about. I think we should only introduce him to someone when we feel it is a long-term situation. Perhaps we can agree to a length of time before introducing him to new people?