I don’t know that it’s ‘mainstream’, in expert circles, for the double of 1H to show exactly 4S. There is at least a substantial minority who play double shows 4+ spades (often 4-5 with other calls for 6+). In any event, I don’t think it can hurt to bid 4C. Partner will play you for a bigger hand with a stiff club and 4 spades but your hand makes up in playing strength what it may lack in terms of hcp. Over 4R by partner, we bid 4S, limiting our hand. We should reach slam opposite Axxx, the heart ace and the diamond king (provided that partner appreciates the value of those very good cards) but we may miss it opposite A/K/K. 4S makes it very difficult to reach slam, imo, and is an underbid One possible argument is that 4C allows LHO to double with support but not a strong desire to bid 5C himself…now RHO may bid 5C over 4R. However, I think that might help us. Our 4C sets up a forcing pass.