Check the ground for the injectors (probably on the firewall, an big bundle of brown wires under a bolt). It's behind the battery on the W108, but I don't know where on the W116. They fire in pairs, so if one works, the other in the pair should.
Other things to check are:
Injectors themselves -- they do occasionally go bad. Resistance across winding should be 2-3 ohm.
Trigger points in the distributor -- but as I said, the injectors fire in pairs, so either two or four should be out, not three. Four "points" under the point plate in distributor.
Rich running can be caused by a loose temp sensor wire to air cleaner (easily pulled off, I've discovered), a bad coolant temp sensor, or loose wire there, or worst, at bad MAP sensor. $375.
Bad throttle position sensor.
Cold start valve sticking open, will make for very rich running.
One final thought -- if you have an ignition problem (cracked wires, for instance, from changing plugs) you may be running rich from low vac -- this system doesn't measure air flow, just calculates it from MAP and throttle position.
I've been looking through the Bosch manual while writing this, and it sounds like you may have some bad injectors. The plugs will be burned on the cylinders with faulty injectors if they don't open properly, but do deliver enough fuel to ignite (lean running only on those cylinders). When the quit completely, you ened up with a rich running condition because of low vac and large throttle opening.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!