You can definitely find them, but you have to search a little harder since you're doing your own legwork. Princesses with really nice cuts are more likely to be sent to AGS for grading because they'll get that coveted ideal cut grade, whereas the GIA stones tend to be a lot more hit-or-miss. You may have to compromise on color, clarity or size. Let's say you're shooting for a 1.5ct G/VS2 (just for example). You look through 20 or so stones and find one that has a killer ASET, but it's a 1.4 H/SI1. That may be the one for you even though it didn't fit your original parameters. You just might have to stretch them a little.
If you're open to buying online, definitely check out James Allen's inventory. They have mostly GIA stones but they offer ASETs on up to 3 stones. When I pick out princess cuts for people from JA, I first narrow it down by color/clarity/size/budget, then I look at the photos until I find one I like, then I suggest for the person to ask for ASETs of those stones and post them here.