Hi! Thanks for the reply!
I started from scratch with all amp EQ. As I say, the tonality of the pickup is great, but the hum I'm getting is too much for me to tolerate as it is. Pickup selector goes Neck>Series>Parallel>Bridge. The neck position is as noise-free as ever, as is the parallel (standard tele middle) position.
It might be worth mentioning that I have a stainless steel scratchplate, and all pickup cavities are shielded with copper tape. So there is more than the usual potential (ha!) for earth loops. (Irrelevant explanation: The scratchplate is grounded through the bridge pickup screws, and through a spur of copper foil that comes up from the bridge pickup cavity shielding. So there is an earth loop that goes scratchplate>pickup screws>bridge pickup baseplate>black wire>back of volume pot>shielding/bridge/strings earth wire>shielding>scratchplate. However, this loop has always existed in the guitar, and has never been a problem with the previous two bridge pickups. Since the black pickup wire and the global ground wire are right next to each other for the whole 2 inch journey to the volume pot, it's hardly a loop at all.)
I'm stumped.