I have the STK-S9 in a MIJ alder & rosewood Strat. I haven't had the JB Jr to compare it to directly, but I've had the full-size JB a few times, as well as numerous single-sized humbuckers and stacked singles, including the Hot Rails, Tele Hot Lead Stack, and Chopper T. Never had a YJM or know anything about that, I'm afraid.
I got the Hot Stack Plus specifically because I wanted to preserve the original look and some of the single coil tone, but have something that would mesh with mild distortion smoother. It certainly does that, but how it does it depends on the distance from the strings. I have never had another pickup which changes sound so dramatically just by raising or lowering it a couple of millimetres.
Close to the strings, the output is about equal to an 'overwound PAF' style humbucker, like a 59 or a Gibson Burstbucker 3. It's louder than the Tele Hot Lead Stack, but noticeably quieter than the Hot Rails, and slightly quieter than the Chopper T. The EQ balance is like a fat, overwound A2 humbucker, too. In fact the closest pickup I've had to it in tone is a Burstbucker 3 (42awg 8.8k, A2). Darker and fuller than the full JB, and not as loud. The note attack is a little sharper than a typical humbucker, but not so different that you'd notice it if you weren't listening out for it. Really even and smooth for anything from totally clean to fairly heavy distortion by itself; add on any flat-toned overdrive pedal (BD-2, BB Preamp) and it is totally indistinguishable from a humbucker. With the Hot Stack Plus close to the strings, I treated the guitar like an HSS, and it did that job perfectly well.
That wasn't actually the sound I was aiming for, though, so I lowered it just a tiny bit—about 1.5mm on the treble side and 2mm on the bass side—and that totally changed the sound. Now it sounds a lot like a Jazzmaster pickup, and far less like a humbucker. It has the string-to-string separation and clarity of a normal Strat/Tele/Jaguar pickup, but the fuller sound and smoothed top end of the fat Jazzmaster coils. The note attack has sharpened even further. The output is about equal to an underwound PAF-type, in my case perfectly matching a Fender Shawbucker 2, and just a bit louder still than a Texas Special. The #2 position (with a Vintage Hot Stack Plus STK-S7 in the middle) now 'quacks' like any standard Strat. Just like a JM or an underwound humbucker, it's smooth from clean to medium distortion, but heavy distortion is a little screechy. However, using a mids-heavy overdrive pedal (SD-1, Klon, etc) into medium distortion allows it to arrive at heavy distortion with the same smoothness that it had when it was closer to the strings.
So, for you I can recommend putting it quite close to the strings. It probably won't match the JB Jr, but it'll sound much fuller than any other single or stacked pickup, and since you're using a Kemper you can freely dial in as much distortion and fullness as you need, anyway.
The only thing to note which might separate my experience from yours is my guitar has the bridge pickup wired to a tone control as well, and uses a 50s-style 0.1uf cap as opposed to the modern standard 0.047uf. This means even at #10' my tone control is rolling off a little more treble and even some high-mids than with most Strat bridge pickups. Also, I have the bridge completely screwed down and immobile, which also contributes to a slightly fuller tone; overall this guitar is fairly dark and warm by Strat standards. A much brighter guitar, like one with a fully floating bridge and no tone control on the bridge pickup, might have a very different experience with this pickup.
Of course, adding a tone control to the bridge pickup and/or throwing a 0.1uf cap in there is easy, if you want to tame any harshness your guitar has.
As the others have said, you can't change the cover on the STK-S9. I also found that it is very fractionally fatter than the stock Fender single coils it replaced, so I had to open up the pickguard hole with a little sandpaper, probably by 0.5mm or so. It was easy to do, though, and given you can get the stacked singles in all the standard colours, I don't think this should pose a problem or be a reason to not get one.
