Dumbell overhead press could bring your training a little change. How long have you been doing the Stronglifts by the way? Sometimes changing the move a little helps you progress. The dumbell exercise must be done with care and consentration if you're having stability issues with barbell also. Start light and build up. You can test you barbell overhead press after few weeks, and see if it works for you.
Yeah, you lean back a bit, make a little arch to the lower back/keep the spine neutral. The point when the barbell is overhead, is it that it's supposed to be in line with the spine. Here
is a good video to recap all points regarding the form, altough it's a bit humourish. T-nation also has lots of good articles around the movement.