I realized in a discussion on BBF that I had not ever mentioned another concept (I don't think, anyway) that you might like.
The auction starts with a raise of a major (presumably constructive), Opener now bids a natural suit, ostensibly GT but potentially ST. As I mentioned in Cuebidding at Bridge, I like 3NT as a power "focus shift" showing 3+ "key cards" (6KCB, ncluding Q's) and a fit for this new suit, suggesting a focal shift to possibly pursue slam.
With a lesser hand, but still cause for a focal shift, one can use a "courtesy focus shift," typically two key cards and a side King, where Opener needs shortness to make this interesting.
When spades are the agreed major, 4C is the "courtesy" focal shift, allowing Opener show either suit as shortness and agree the focal shift and slam interest.
When hearts are agreed, 3S serves this function, to get below both minors.