7.5" is typically the shortest "common" barrel and the same upper that is used on AR handguns. I have had good luck with two Model 1 Sales uppers on the M16A1. The upper is $385 plus $120 for a bolt group. However, form most SBR type uses I would go with a 10.5" and possible one from LMT or similar.
At least one company made one an inch or two shorter but was a very high dollar item with special buffering and gas system.