Spent a few days researching and have come to the conclusion that it's supposed to sound like that.. Neck and middle on the SS are just fantastic but I can't live with the bridge pickup. Strat bridge pickups are, I reckon, hardest to hit the target but I'll work on it a while and if all else fails I'll go down the pickup rabbit hole.
Other observations. The volume taper is very steep and it's all but off by 5. And the holes in the trem block, being so deep, might usefully have a chamfer to assist in threading new strings through. Small stuff on an otherwise great guitar.