Mounting a ceiling fan with 28” joist spacing and no attic access
I had to install a light fixture over a pool table in a situation very similar to this. The fixture had to be centered over the table and between joists with 26" space.

I cut a 2x4 23" long and two pieces about 5" long. I centered the two pieces on each end forming a "T" and screwed them in with  some 3" deck screws. I pre drilled two holes at each end of the two smaller pieces for fastening into the studs and fitted each hole with a 3"deck screw. Now comes the tricky part. I cut a 10" hole in the ceiling and was able to fit the framing between the joists and centered the 2x4 and was able to screw the screws in with a ratchet screwdriver. I fished in some Romex and installed a fan box. I used the cutout from the hole to make a quick patch and then installed a 12" fan medallion which cover the hole (see below).



They come in many styles. Hope this helps