Just when you think it's going well.

[JLOGIC]

Here's an idea. You play 1♠ as 11-15 with 5+ spades, right? And 1♣ - 1♦; 1♠ is 16-20ish with 5+ spades. Well you could just play exactly the same system for both but with 5 hcp transferred from Opener to Responder for the second. Then a 2NT response will probably show a good spade raise. Easy. For anything more complicated it would probably be necessary to know what you use 2NT and 3♣♦♥ rebids for now. Most likely one of these could be absorbed into something else in order to free up the bid to show the super-max spade raise that cannot splinter.

 

I find using 3x as a good 6 card suit and nothing else to be useful (KQJxxx AQxxxx etc) for getting to 3Ns that could otherwise not be bid. I have a way to show 6-7 and a 6 card suit also, but this hand type is a lot different since if partner has the other honor you probably want to be in 3N. The main priority after 1C 1D 1S must still be getting to light games, I think using 4 bids on slam hands would be inefficient and prioritizing thigs wrong.