I had a Winchester model 97 16ga that was old enough to have the 2 9/16 chamber reamed out to 2 3/4 some years back. This was before I found out that you can buy shotshells that are made for the shorter chambered guns. Since the longer 2 3/4 shells don't always eject out and sometimes get hung up, there is no issue using the shorter 2 1/2 shells is there?

You are good to go.   There is no problem going with the shorter shells.

QFT