You're on a tonequest! This may be incurable.
SD 59s are decent pickups. Schallers are as well. If I could only have one pickup, it would be Fralin P-92s. That is not to say they are the best. I just like the single coil-like sound. The same is true with the Z-coils from G&L.
There are innumerable variables in the signal chain and output. Strings, picks, technique, harness, control settings, cable (maybe), amp and its settings, speakers, position of speakers to the ears, and room or hall environment. Then there are pedals.
The electric guitar has been around close to a century. It is funny that one of the great choices in pickups with jazz players is the very old Dearmonds. https://dearmondpickups.com/
If pickups were cheap, I'd like the idea of popping in a different set with string changes. There could be mini-toggle switches to change the circuits internally.
Heritage semi-hollows are not so easy to change harnesses on. And pickups are not cheap. And your ears and brain are different than mine. So this could be a terminal journey, worth every step. Enjoy it.