Dave/Paul
First Sixth Edition does not have support for either the 11/23 or a floppy. So your issues might be found in either place. Where did you get the modifications? Maybe:
https://www.hamartun.priv.no/v6unix.html Your guess WRT to floppy being the source, would be where I started to poke.
Frankly, early UNIX when ported to a system with a floppy has a lot of issues [we did this at Tektronix in the early late 1970s for the magnolia and some of its siblings). Take a look at the physical floppy - you will notice a lack of magnetic material near the center of the diskette. This is the i-list and v6 (and v7) hits it pretty hard. Caching of the inodes was added later, but was thought to do on the 11s due to lack of address space [you need to BSD 2.X later versions and generally need support for separate I/D 11 and a lot more physical memory].
I thought I remember that the 11/23 is a 11/40 class processor, not a 45 class so it lacks the '17th' bit as it were, although I think it can support more the 256K bytes of memory, but again it takes hacking V6 to enable and use it.
One thing you could do is put the kernel image on simh [
https://github.com/simh/simh] or Ersatz11 [
http://www.dbit.com/] and try it with an 11/40 and an RK05 emulator instead of the 11/23 and floppy since 11/40 with an RK05 and RP03/04 were the native distribution. Then try to change processors, and finally disks on the emulation. BTW: it if works fine with an emulated floppy [I would not be surprised if it does] I would look at the driver. I would think that it is possible for the floppy driver is causing the 11/23 to have missed interrupts with how the spl()/splx() calls are working [which can get tricky and easy to be 'almost right'].
One other thought, I'm pretty sure that Noel's V6+ system from MIT can support a 23 but I don't know about floppies, you might try his image. Check out gunkies -
https://gunkies.org/wiki/UNIX_Sixth_Edition, but Noel might reply here directly with more info.
Have fun.
Clem