I'm a tenor/bari player who took up alto for the same reason you did. Never a squeek on the big saxes, but I sometimes squeek on alto if I'm not careful with my cheeks and the area below my lower lip. I think I puff them a little to get a fuller sound on tenor and bari, but the alto won't tolerate that abuse. This may or may not be accurate (i.e., it may be total BS), but that's what it feels like to me. At least when I concentrate on it there's nary a squeek on alto.