Well no one else seems to be willing to chime in here so I will try.
I know you were pretty thorough on your descriptions but I would like some additional info! Is it the solenoid the battery is connected to or a battery isolator on the fender well??
This is a diesel right? If so spray a little WD40 down the air intake, it acts like starting fluid for a diesel, Like starting fluid on a gas engine, don't over do!
Is the new starter dragging right from the start? Or is it slowing with long periods of cranking? Starters will slow with extreme heating from extended cranking. Like a diesel in my old service truck or the 18 wheeler tractors (I sold) is it supposed to be a 24volt setup? I have owned both, diesels with 12volt starters and 24 volt starter systems. Has someone changed the setup? the box the new starter came in should state the voltage for it.
I don't have manuals yet to look up what you have.
Are you certain the batteries are good? They may be on the last leg before failing and can pull current off of you jumping system as well!

You could only see this under load testing. If it is a 12 volt set up switch the batteries, the one your starting off of may be weak, the other could be better. One weak one in the system can cause drag, if they are in parallel. Then the system needs the extra amps to crank over the motor and may not have it!
I have a glow plu question but, I am not certain this is a diesel. If it is are you allowing the glow plug light to go out prior to cranking over? Is the glow plug indicator lighting?
If it is a Diesel you may want to list this in the Diesel forum, a lot of those MB lovers don't seem to hang around here, must be the gas fumes they are afraid of!