I wanted to top this as I figured out why the handle was not operating properly and how to fix it in approximately ten seconds! Hopefully it'll save some other W124 owners a whole world of messing around...
Long story, short: I've been parting out an E420 for a buddy. While doing that, I decided to take the driver's door apart to figure out my problem.
I pulled out the entire door handle mechanism from the inside:
Note the cream coloured plastic crosshead piece. When you turn that, the metal arm above it adjusts inwards and outwards.
That crosshead is normally accessible from the lowest hole of the three covered holes in the door (pictured above). So, all you need to do to fix your door is remove the rubber bung and adjust the screw until the door opens normally. No need to take apart the entire door like me
That's it. Easy as pie thanks to Mercedes' excellent engineering as always. If only I knew this four months ago
