Most of the chamber difference is in the "leade" (taper from chamber to rifled bore). This guy sells a 5.56 chamber reamer that cuts the leade area only and won't harm the chamber shoulder area or damage the rifle's headspace. Should be just the ticket.
Of course, if you've been shooting 5.56 ammo in it all along and never experienced any overpressure problems (see link), then your chamber may be fine as-is.
Thanks. Is there a way to inspect the rifle for “damage?”