For a square body, round hole, a custom gage is what you will probably need - calibration certs from the maker. Van Keuren was the/a major player in "round stuff" including "ring" gages, and custom builds - but half a century ago.
Go ogle finds more than one present-day host, so I am not sure if the survivors are dealing only through others, or were broken-up, various segments OWNED by others.
Plain round external, cylindrical bore ring gages, setting rings, bore gage setting masters, are now also stock items from Mitutoyo et al.
Can you not use a cylindrical external shape, rather than square?
The bore has to be as "perfect as possible", but how critical is it that it be perfeclty centered if set-into a shop-fabbed block?
Mind I'm "guessing" that the need for a rectangle is because it is on a milling center's table, vise, fixture, pallet, indexer, rotab, or tombstone or somehow meant to tuck up against a straight edge or into a corner?
"Special need" one way or the other?