Tom, I'm still not at all sure I understand the support system under that floor. I see where the joists are (I think), and kinda what sizes are where, but I don't see what's supporting what, as it were.
I see your neighbor has a wall directly under part of it, which is a good thing, but that's the onliest support I see mentioned.
And I'm still much confused about the function of the iron straps we see above some of your joists. I see no such stickin' out the bottom of the upstairs neighbor's joists. Is just on accounta I'm old and blind, sorta?
All I'm lookin' for is:
1. Is there still enough structure under there to support the very substantial dead load of a very thick mud bed installation?
2. Is there enough support under the structure to make it a viable candidate for re-creating the very substantial mud installation it had before?
If yes to both, I'm still in favor of covering everything with mud to create a flat (and maybe level) plane and doing a reinforced mud bed on top of that.
[Edit]
And I typed all that before I saw mention of a joist spanning 20 feet unsupported. Would certainly wanna know more about that there.
My opinion; worth price charged.