I had one in the finish you sought - I accidentally killed the preamp so got a passive loom. Worked really well. So comfortable to play with such a perfect balance. I eventually decided the neck was too skinny for me so sold it. Maybe I should have kept hold of it 🤪
Not sure where you are in the world, but Newtone strings in the UK will make a custom set for you. Might be worth a look when you next need a new set for the 38” beast!
The only jazz version I had was ash bodied, and was heavy as hell (sounded awesome though).
Had a PB50 that @yorks5stringerhad sprayed LPB nitro and that was ace (just decided single coil Ps weren’t for me).
I would summise that the weight is all in the body, but also some of the sound might be, too?
I surprised myself with how easy it was to make a scratch plate. Bought a blank from eBay, made a paper template, cut out with a jigsaw, finessed the shape with a bit of sand paper, edges beveled by dragging a blade over them at a 45% angle.