Alembic.
Look for a used one. In my view, a primary consideration will be neck taper; and for most Alembics that will be either classic or comfort taper. My preference is classic taper. I couldn't do the things I'm doing with either my right or left hands on a comfort taper. But that's me and my style of playing; others of course couldn't do what they're doing on a classic taper. I'm very happy with my 34 classic taper six string.
After that, the electronics package will also be key. But when cost is a significant factor, just getting an Alembic with the taper and scale length you want, and getting that Alembic tone from those pickups into your rig or recording console, is a great starting point.
Also, your idea of a five string E to C is a good one, especially in light of what you are doing with chords. In the songs that I play I use my B string a lot, but it is capo'd at the third fret and I am primarily using it as an open low D. Of course it does come in handy when playing regular bass lines or doing extended runs across the neck. And I do practice incorporating the B string into chords; but those are still a bit difficult for me to hit, and they haven't yet become part of any of the songs I'm playing. So a five string would be a good option.
But I can't recommend anything except Alembic. They are the only instruments I know anything about. I played a G&L L-2000 from around 1980 until January 1996 when I got my first Alembic. It was night and day. I haven't played anything but Alembic since. Sixteen years.
So perhaps not the answer you were looking for. But for someone like you, and I really like a lot of your tonal ideas, I think it worth considering getting the best quality tone as your starting point. And Alembic pickups are the perfect canvas for the tone shaping you are so good at.
But of course budget realities are important too. And lots of great music has been made on things that weren't Alembics; or at least that what someone I met in jail told me. Or maybe it was great books written on cheap paper. Hmmm, can't really remember; it was a long time ago.
