** the burners have somehow been knocked out of level. I have tinkered with what I thought was a leveling screw where the burner is attached to the cooktop, but that hasn't had any effect. **
I've never seen a "leveling screw" for the surface elements on any make of kitchen stove. The screw you're referring to is likely the hinge screw (for the element to 'flit up' for cleaning beneath) and which also grounds the element to the rest of the range.
If the element is not sitting flat, the trim ring or drip bowl may be out of place or the incorrect ones for use on your model. The only other cause I can think of is the element's frame is bent/melted in which case the element may need to be replaced.
You can see some popular GE range surface elements at the following link: