A bit of an update.
After reading all the advice from you guys I decided to buy a set of GF humbucker pickups for my LP. I sat down with a beer and a credit card and started to browse. Next thing I knew I'd bought a set of '63 Tele overwound pickups (7.8k bridge and neck) for my Mexican Tele.
Now, this was not what I had in mind but an impulse is an impulse so....
A week and a half later they arrived (not bad delivery across the Atlantic). I'd never soldered anything properly before let alone changed a pickup so, after watching a couple of YouTube tutorials, I settled down with a mug of tea and set to work. An hour and a half and quite a bit of foul language later they were fitted and working.
What a difference. All I can say is thanks for suggesting GF. They're powerful but you can still hear everything. They push the amp beautifully without sounding shrill, even on the bridge with the tone wide open. I've played them live a couple of times and, at volume, they really growl.
So, after I've got January out of the way, I think I'm going for a set of GF Alnico V Humbuckers (in the zebra case).
Unless I get another impulse..