Oldfed, there's not a nominal 2 3/4" pipe size; pipe goes from 2 1/2" to 3", which are too small and too big for what you are ideally looking for. Your only hope (small) would be to find 3" outside diamter round steel tubing with a 1/8" or 3/16" wall thickness. It's commonly made, but not usually sold in pieces as short as you need. A fabrication shop might have some, or a machine shop, but you could spend a lot of time looking.
I like the previous ideas on here about going with a smaller size and through-bolting it, or using 3" pipe and either splitting it lengthwise and clamping it, or filling it with tamped-down sand.
This Forum is a wealth of creative, practical-minded folks!
Oh, and FWIW, a piece of 3" square tube with a 1/8 or 3/16 wall probably would work, too, especially if you're going to backfill it with sand. Round peg, square hole, but still..... Might be easier to find at a fab shop than the round steel tube, but all in all, pipe is going to be your best (and cheapest) option I suspect.