This type of padded gambeson was still used on XV century but by then it was usually called a "jack". Indeed the best representation that we have of the underarms opening do came from the famous XV century painting "the Marthyr of St Ursulle" by Memling 1489.  Of course, by then the jack was worn with mail voiders underneath...   but this precaution is no longer necessary on our fairplay XXI century battlefields !  ;)