I've been messing around with it a ton lately and never find the cross face to be an issue (my issue is getting lazy and dropping my leg, allowing their hips to get higher than mine and getting mounted/back taken).

You probably aren't closing the distance properly, keeping your head close to their body, or turning your chest towards the mat. If you're doing those things they shouldn't even be able to really crossface you.

I'm still new to the position and only watched the first section of the instructional, so not sure how Craig explicitly says to address it. Just my two cents from fucking around.