Some of this is a repeat of what you did but it is fast to check it again.
Do this with the Voltmeter.
If you Pull out the Electrical connector from the Alternator the 2 large slots on the Connector should have Battery Voltage all of the Time. On mine those are the ones the Fat Red Wires go to.
On the Smaller Single Slot you should only get Voltage to it when the Key is on and you will get slightly less than Battery Voltage due to the little Charging Light Bulb. That slot is the one that has a Blue Wire on Mine and goes to the Charging indicator/Light.
If your Bulb had been no good you with the Key on you would have had no Voltage at the small single slot.
If you know the Bulb is good but you are getting no Voltage when the Key is on it could be the Ignition Switch.
Also some sources say that the Bulb needs to be 2 watts and others say 3 in order for it to have enough resistance to excite the Alternator to charge.
As you noted the Alternator needs to have a good ground in order to function properly. Cleaning the Chassis to Engine Ground Cable and the Battery to Chassis Ground cable contacts normally takes care of that; except the if your Alternator Bracket is line mine where it bolts up to the Engine it is extremely rusty.
Rust does not conduct Electricity well.
To see if that is the problem People take one Jumper Cable and connect it to the Negative terminal of the Battery and then find a bare metal spot on the Alternator Housing and apply or clip the Jumper Cable to the Housing. If you start charging you know your problem is a bad ground.
I made the Test Cord in the below Thread to separate an Alternator issue from a Vehicle Wiring, Bulb, or defective Ignition Switch issue. Only one other person has made one that I know of.
However, the Test Cord does not eliminate the possibility of a bad ground issue. That can be taken care of with the Jumper Cable use I described.
Alternator Test Cord for W123s - Mercedes-Benz Forum