I thought I'd update. I got the fan to work, but I have some serious
cleaning up and adjusting to do. The 36" rod is too long and I barely
fit under it standing upright (I'm 5'10"). The 24" rod is too close of
a call, so I will likely have to cut this rod down and reconnect.

I ended up making a new mount about a foot over from the existing one.
I don't recall why, but that mount that bridges across two beams
wouldn't work. I think it was mainly because I don't have a crawl space
from which to install that; I'd have to slide into the existing, tiny hole.

It turns out the old fixture is in a good spot. This fan came with a
remote, and I think I will pop the receiver into that old hole.
Normally, it would mount on the kit's fan mount, but I am using an
angled one instead. Having nowhere else to put it, I'll try the old
hole. So everything will have its place.