@Revelation The Custom 22 is a different beast to the 594. I cannot tell you which you would prefer and the ONLY one who can is yourself. The Custom 22 is a bit more Les Paul like than the Custom 24 but that's because of the Pick-up positions so the neck PU sounds a bit closer. Its thinner (like a Custom 24) and, if you are buying new comes with a trem bridge too. Its a 25" scale length as well and comes with a 5 way blade to give some different sounds than a Les Paul offers - either both split humbuckers together or the neck split with the bridge humbucker. You can kind of get that from a 594 using the tone pot push/pull whilst in the middle position.
As I have said, the best PRS 'strat' is the Silver Sky for the Single Coil tones but you are adamant that you have that covered. In my opinion, the majority (of not all) the Split coil options from PRS isn't to be a Strat or a Tele but to offer the musician more tonal choices and/or tones that will cut through a mix better because the split coil tones are not competing with Bass, drums or even a second guitarist. Its not just about having 3 or more guitars in one but more about giving the musician more options to be creative with, to fit in a mix etc.
If you have a double humbucker LP type, a 3 single coil strat type, a tele type and the hollowbody 335 type then you basically have everything you need to be a cover band musician. PRS may have models that are of the highest quality and quite a few models that are quintessentially PRS. Some may cover the same ground you believe you have covered so unless you are willing to double up or have something that can offer more options but still has a few that you already feel you have, then perhaps you won't find something.
You already have a Les Paul so why look at the Custom 22? It could replace your LP and offer a couple more tonal options as well as Trem bridge. Perhaps less risk of headstock breakage and better tuning stability too but you may find its not different enough or being more modern, doesn't sound quite like the LP you have become accustomed too. Its still a 22 fret double humbucker type guitar that covers some of the ground your LP does. You may not like the split coil combinations because you have a strat for that.
Just owning a PRS for the sake of owning one and not wanting something you already think you have covered is not going to be easy as there are areas that all PRS guitars offer that other guitars can 'sit' - even if the nuances of the guitars are different. On the one hand, you have mentioned the type of guitar (at least the sounds associated with certain Artists) but dismissed the guitars that are the best fit. You dismiss any split coil tones because you have a strat and you might as well dismiss all humbucker tones because you have a LP. Guitars like the Cu22, McCarty and 594 are alternatives to a LP in a lot of ways although a lot of us will like the nuances each offers and may even own a LP too but if you are limited to the number of guitars you feel you can own, unless you are prepared to double up, to trade for something that can replace what you have and maybe do more, then you may find that the 4 guitars you own already give you what a lot of PRS guitars offer. Its likely to come down to whether you prefer the guitars you have and their role in your toolbox or whether you prefer the PRS guitars and any extra ground they may offer.
My collection of guitars, maybe swap the 509 or maybe either the 594 or Special 22 (which is an expanded Custom 22) for a Silver Sky, and would probably cover your entire guitar collection and the songs you play. All that's missing is a typical strat sound. There are P90's or Filtertron sounds I am missing too but could make do. There are so many guitars that, whilst very different can be very alike too. The Custom 22, McCarty and 594 can all be a Les Paul alternative but also be something different too depending on the nuances, the extra options/features, the era you are comparing it to - let alone the feel, the weight etc. Every one of these could be used as an alternative to a Les Paul but also be different enough to justify purchasing along side a LP too.
The point I am trying to make is that maybe no PRS guitar is likely to be the 'one' for you because you feel like you have the area covered by guitar(s) in your collection. Certainly the guitars I would recommend based on the artists you mentioned, the ones I think are best suited, you already feel you own which may make searching for a PRS difficult because they don't fit in with what you like or do fit in but you already have that covered by a different brand.