I had a chance to mess with the derailleur today:
The low limit screw was, in fact, maxed out. I tried re-aligning the cage next and realized the outer plate angles in from back to front. Next, I set the inner cage plate parallel to the chainrings, and shifting between the middle and low rings improved, but shifting to the big ring suffered. I played with the angle some more and got pedal strike at the outside rear corner of the cage, then did some more adjusting, and it sort of shifts between all three. I'm a bit tired today, so I called it quits before messing anything up too bad. I'll play with it some more tomorrow.