Not sure how you’re trying to open it with just a screwdriver? I guess prying it against the other side? That won’t work well. You need to grip the feed lip with pliers of some sort.

The vice grips Dave posted the link to are perfect for doing this, as they wont put gouge marks on the feed lips like if you use regular pliers. And it will adjust the whole lip at once. Yes you can use channel locks or something like that and pry out while work your way down the feed lip on each side, but if you do be sure to put a rag in between the lip and the pliers to minimize any gouging marks.
You only need a Small adjustment. Just a little tweak to each side. Then try it. Maybe you can measure the amount the case sticks out before and after? Might be tough to get an accurate measurement.