Without the bass here, take this that I'm thinking out loud, OK?
Typically, bass buzzes solely in the deep end of the neck means the neck is TOO straight, while buzzing only up near the body end of the neck usually means too much relief.
Overlay this that straightening the neck lowers the strings, and adding relief raises the strings: Imagine as you tighten the truss rod, the head/nut 'sinks' relative to the body, and rises as you let more relief back in.
Plus the closer you get to where the bass starts buzzing badly, it only takes a little too much to cross that line.
I shoot for dead straight and then let enough relief back in to where I can just feel a little room to breathe under my hands, so we are probably looking for about the same feel, not 'behind the frets'. I'll settle for a only a little random buzz here and there occasionally as long as it doesn't go through to the amp, and over a few weeks I'll tune that out. And certainly, out of my five basses, no two are alike, and it's just the way life is that some will just adjust lower than others without complaint.
Two things stand out to me:
1) You bought it used and it still had the ALEMBIC strings. As they're not commonly available around the country, IF they were the strings it came with and it's in mint shape the bass MUST have sat in the case most of the time and probably flat, tuning-wise.
2) Tuning UP cured it: More tension gave more relief and it subsided . . .
IF it were me, I'd try one more thing I learned from the Dan Erlwewine book:
Unstring it. Let the truss rods completely loose. Clamp the neck/fingerboard to a straight board (be sure and pad the board and clamps, a clean 2x4 cut to the length of the fingerboard works fine). Once you're satisfied all 24 frets are touching the board (you can check this with the short side of a framing square, and use a 6 or shorter metal rule to check two or three frets at a time to eliminate any high frets), tighten both nuts to snug and release the clamps.
You've now got a straight fingerboard 'unloaded' and you've probably bought more 'purchase' for your truss rod nuts. Truss rod nuts are for fine tuning, you did the 'heavy lifting' with the board and clamps. Now re-string let her sit overnight or a few days and start over.
Of course if that STILL won't do it, you obviously know where to go. It's problematic in that truss rods have the least effect on the very end of the fingerboard towards the head, generally. But maybe this treatment will help you skip surgery!
Glad you're home!
J o e y