Use some caulking around edges to help grab the box inplace with new box. Hopefully you get one that has the small lip. You could also use spray foam to help set it...but that can make a real mess of things if not careful.

As others have said the issue you might have is where your light fixture attaches to the electric box. If it has the round washer type flange that attaches to box and then screw from light connect to the washer flange, you should have play to rotate new box to get good grab. If the light attaches directly to box, you may have to get creative on repair.