First off, unless you are playing Guitar, I can't see how you can play Orchestral works with 4 fingers in the lower positions and not kiss your hands.
Second, I have found that real thin Necks make me press harder and fatigue my tendons. I am not more comfortable with a medium to slightly thicker Neck for some reason.
And third, there was no Jazz in the early 1900s. These Basses your refer to were most likely made for Students or Dance Bands. The Germanic Shop Basses used for Jazz are usually those that are not good enough for professional Orchestras. Also, many of them are so beat up that they look 50 years older than they actually are. Most of them were made after wwII unless we are looking at the blockless wonders. The older pre-wwII non blockless ones were usually made a bit better but still many of them are machine made with integral Bass bars.
I have an acoustic Jazz Duo gig tomorrow night and will use my 1814 Gilkes. That doesn't make it a 'Jazz Bass' unless it has 'Fender' written across the Scroll..
Nut height is very very important. I have seen too many Basses that were hard to play mainly because of the Nut. A client came here a few months back looking to upgrade his Bass. It was a labeled Juzek German Shop Bass. I offered to re-cut his Nut and tweak his Bridge to better evaluate his Bass as it was to be traded in towards a more expensive Bass in my collection. When I was done he was amazed. Two months later I find out he now loves that Bass better than ever and doesn't need another Bass. It just needed a better set-up. My
favor cost me a sale..
So... D-Neck 41-41.5 is your vote... Sorry for the rant..