Reducing threaded rod to mount fixture cross bar

I have a very antique light on a very antique ceiling that I do not want, by any means, to compromise (meaning have to open). A few weeks ago, the ceiling light that was installed started losing its grip on the flange. The primary structural support on which the light was mounted is a threaded rod that I measured (with a caliper) to be roughly 13/16" in diameter. It can be seen in this picture as the central protruding piece in the middle of the hole, just to the right of the white electrical tape.

That 13/16 is my measurement, which may be off so my first question is what standard size (by which to look for in a store or online) that resolves to as I obviously cannot take the piece with me.

Then I need to adapt this crossbar on it. The smaller size of the hole on the crossbar is why I need to reduce the threaded rod from whatever standard size it is (part of my question) to this:

In order to mount this flange on which the light goes

QUESTION 1: What standard threaded size is something that roughly measures 0.82-0.84" (roughly 13/16").

QUSTION 2: Is adapting this rod down to a modern stock size my best approach to secure this flange to the rod?

NOTE: This surrounding context of this terminal is what I have to deal with as invariable. Suggesting to change the installation because it is out of date (so that I can install a proper, modern box to which adaptation is easy) would be kind of superfluous as I am not touching the ceiling. This is a retrofitting job.