I know it may seem very perplexing but I can assure you that you are not in the twilight zone. I think I can help explain.

An 8 inch rim is only 8" wide at the beads.

The rim is really/actually just about 9" wide (from lip to lip)

Backspace is measured from the mounting surface to the inner lip, not the bead seat.

The trim ring is 2-3/4" deep, yes. But should be measured from underneath the lip because the lip of the trim ring sits on top of the rim lip, which remember is 9" wide. About 1/8" of that trim ring is sitting completely outside of the rim.

The rest should spell itself out.

And doing all that math you were doing, with adding everything together to try to get a total of 8" may not be accurate either because who's to say that the spokes (or inner part of the rim we are measuring the gap from) sits exactly where the backspace is measured from, so don't rack your brain on all these fractions and math.

I have it sitting in front of me on my work bench. The trim ring is seated fully. The backspace is 4-1/2". The trim ring is 2-3/4" deep. And there is still a 1-1/2" gap. So I just need to figure out what to do.
Considering trying my hand at making a trim ring out of some stainless, if for nothing else, just for fun. Does anyone know if these things are pressed into shape from a die? Or cut from flat sheet metal and rolled into shape, then welded? Hey if I'm successful I can go into business : P