the sh-6n does grab my interest. Does it split well? I am not really into swapping magnets so i have not tried the jazz modded but have tried the others you mentioned and they sound great but do not split well?Distortion neck comes to mind. IMO it is big and bluesy, though YMMV.
Have you played a 59 neck? -a Full Shred neck? Have you tried a Jazz neck with an A2, 3, or 8?
lookin at the spec's of the sh-6n it seems to be a good canidate for splitting (12k full and 6k split) a real single is around 5k-6k so one would surmize that the sh-6n would be a truer single coil tone than a jazz or 59 neck which are both around 4k split. and IF i need the tone to be more warm i could try a magnet swap to a alnico 5 like the JB has?I thought of the Distortion neck too, it's the closest thing I've tried to what you're looking for although I've not tried every neck pickup SD does.
As for splitting, I have an SH-6 bridge model which splits and it works great, but I haven't done it with the neck version.