I have a HSS setup in my Pacifica 612, with a Duncan JB in the bridge and 2 stock single coils. I like the sound I get from a bad monkey with no gain into my AVT on the clean channel; I've just been getting into jazz lately and the pickups i have are more for metal-ish cleans. So, I want a single pickup (not for any kind of distortion) that is good for nice clean jazz sounds. Budget is under $200 AU.
You could try a lace sensor blue in the neck; it's got that nice warm sound but still single coil clarity. I really like it.

Maybe also try a single out of a tele's neck? dunno how that'd work out though. Lipstick pup i mean.
Fender Highway 1 Strat
Agile Septor Pro 725

Fender Hot Rod Deluxe
Axe-Fx Ultra

Trust me, I'm a medical student