PART ONE
OK.
By comparison to the guitars you're recently bonding with, the SE Standard 24-08 differs in having a scale length .25" longer than the Ultra Viking and .4" longer than the Duo Jet. Doesn't seem like a lot, but I consistently find it tonally significant in brightening tone (and stiffening the feel at least a bit). And it's not just a matter of brightening the high end; the focus shifts to higher frequencies throughout the spectrum. To illustrate by extremes, a 25.5" Fender with humbuckers sounds brighter and harder than a 24.75" Gibson-type with the same 'buckers - and still sounds like a Fender. The opposite is true: a Fendery single-coil on a Gibson-scale instrument sounds "darker" than on a Fender, and the Gibson still sounds Gibsonny.
The 25" scale length is simply its own animal. For years I disdained it for being neither GibsonFish nor FenderFowl, as though it didn't have its own character. Changing ears, changing taste, over-saturation with the usual scales, whatever - but now I find that middle ground attractive and tonally fascinating precisely because it does mix the two polar species. Its tone can point toward Gibson (as shorthand for 24.x" scale with 'buckers), and it can point toward Fender (shorthand for 25.5" scale w/singles) - without getting all the way toward either one. When playing 25"-scale PRSeseses, I find it most fruitful to forget about those endpoints and enjoy it for what it is.
The 24-fretness of the 24-08 pushes the neck pickup away from the warm harmonic sweet spot it usually occupies on 22-fret necks. (Like right where the 2-octave harmonic is located.) To my ear, this has as much effect on the overall tone as the scale length - but "only" if you're using the neck pickup or the middle position; it has no effect on the bridge position. (I say "only" because I use neck only or the middle position at least as often as I use just the bridge, so it's significant to me.) My personal take on 24-fret guitars has always been that they sound thin - or at least "less full" - than otherwise identical 22-fretters. I prefer 22 frets, and most of my SEs are 22s.
That said, I've come to terms with the less bottomy overall tonality of 24-fret designs, and appreciate them for their frequently more manageable behavior at higher volumes, with higher gain structures, and with more saturated tones, where they automatically roll off low end which can muddy and fart out the proceedings. They're a bit like rolling the low end off at the amp or with an EQ. And on the other hand, when I feel a 24-fretter sounds thinner than I'd prefer in a cleaner setting, it's easy to add some low end the same way. You don't get exactly the same contour you'd get from a pickup under the 2nd-octave harmonic, but you get close. Also, I just know not to pick a 24-fret guitar when I want that low end warmth. Which is why I tend to 22-fret necks.
So you have those two factors going on with your 24-08. You don't say if you have other 24-fret guitars, or have experience with the 25" scale - but the guitars you mention are both 22-fret 24.x" scale. If that's what you're liking these days, the PRS is going to be fundamentally different by design, and you shouldn't expect it to work just like them.
Other fundamental build differences: both the Jet and the Hag have maple tops and mahogany necks. (On the Swede, over a basswood body; on the Gretsch, over a "chambered" mahogany body.) Your SE has an all-mahogany body with a maple neck. In a conventional analysis, I'd expect the all-mahogany body of the SE to be a bit warmer than a maple-over-anything sandwich - and the maple neck to be a bit harder and brighter in tone than the mahogany necks. I have both a Standard 24 and Custom 24, and hear that difference myself. So does the maple neck on your 24-08 bring back the brightness the body softens? Don't know. The materials recipe could be a wash.
BUT. If the guitars which currently most tickle your ear have 22 frets and mahogany necks...maybe you didn't pick the right SE to test the PRS waters with. You might be happier with a Custom 22: still 25" scale and still maple neck, but you get 22 frets and the maple over mahogany build. I prefer the semi-hollow version, for just enough more body resonance. The C22 isn't currently in the SE line, but it was last year - and used examples abound.
Or you might prefer the Zach Myers model, which has the whole package you seem to go for: 24.x" scale, maple over mahogany body, mahogany neck - AND a semi-hollow build. (Similar to the Jet's "chambered" body.) The 245 pickups in that guitar are also more tonally balanced, less pushed toward the bright end of things than the pickups in your 24-08.
The 24.5"-scale Santana model would be another candidate. The current version is 24-fret, but it's come as a 22 in the last several years. I like both, but slightly prefer the 22.
I know you're asking what pickups you can swap in, and other guys may have responses to that. As it happens, I'm enjoying PRS pickups as something different from the general run of humbuckers; I think they're part of the recipe, and well-matched to the guitars. Doesn't mean you shouldn't change yours - and there may be a set somewhere that will turn the 24-08 into something you like a lot better. But you'll definitely be compromising the PRSness of what is a very specific PRS recipe in a guitar that might not have been the best choice for you from the start. Specifically, the pickups in the 24-08 (I think; the evidence is ambiguous), with their TCI designation, are the same as the pickups in the SE Paul's Guitar, and have the most convincing split to single coils I've heard in any modern humbucker. They're kinda special. (And if you rip yours out, I'll take them!)
For what it's worth - and it's probably been mentioned in the thread - I find that to get the humbucker tone I'm used to from a PRS, I back the tone down to somewhere between 6 and 8 on the dial. (Though I often leave it wide open, because I like that the PRS has a brighter, more articulate 'bucker tone than most comparable guitars.) And when I have the pickups split to singles, I have to back the tone down at least to 5-6, and sometimes lower than that. Otherwise, it can be Plink City, and remind me of an old piezo in an acoustic, plugged into an amp with the lows rolled off. (Unexpectedly, though, the brighter single-coil settings can sound great with dirt. Or I could just be old and deef in the high end.)
Also...before you swap out the stock pickups...if you haven't yet, experiment with pickup height. Try both directions. It makes a difference. And I'll assume you've twisted knobs on your amp to find tones you like out of the PRS. (I won't say "make the PRS sound like your other guitars"...because there ought to be a difference, right?) And to fundamentally re-voice the guitar, try pure nickel strings rather than the XLs (which are also my default string). I put pure nickels on guitars that seem overly bright and strident to my ear, and it works to round off the edges.