I haven't read the whole general discussion in full so this might have been talked about, but after post on hit nutpuch or off of a jump in I was looking at a lot of his strings and found quite a bit of good options and staggers aside from 1,1 and what not.
I understand 1,1 can be used to chain into the low, but for sustainable pressure if that's what people are going for that doesn't require stamina, mixing in 1,2 which is listed as plus on block, back 2, which is mid and listed as plus on block and 2,1,4 which can work identically to how 1,1,4 works except for the fact that it's not duckable mid combo and leaves you right next to the opponent on block and is also neutral too with similar chip I believe. The more variance, the more likely the pressure will be sustainable and throws will connect too as well as other mix ups working as opposed to a more linear approach.
Then there's 1,2,1 for spacing and to mix people up on when you're going to go for throws or low pokes and on hit you can go into stunt double call. There's just no reason not to vary your pressure since all these options don't require stamina, are safe and in some cases plus and leave you right next to the opponent to keep the pressure going on them.
Just spit balling at the moment and testing things, but I love this character, Cage hasn't been this fun in a long while so I've been playing him a lot, but only Stunt Double, not really interested in the others, even though Fisticuffs looks really good.