Here's a crazy thought that I don't think anyone mentioned...
Have you checked the brushes on your alternator? The brushes on my 145 were ground down to nothing leaving me with no electricty and a dead battery. A local mechanic made me some new brushes and I was happily on my way.

Also, what sort of alternator is this - SEV/Marchal or a Bosch Unit?

Unless you have a newer alternator, your voltage regulator ought to be on the fender, not the back of the alternator. Even the 1st year of the 240 (1975) has an external voltage regulator so you probably have one. You're probabaly looking at the capacitor or the plate that's covering the brushes. The red wire ought to be coming off a semi-circular black plate with two bolts on it. The wires should run up to a oversized relay-looking thing on the fender. Looks for DF, B+ and D- embossed on the metal of the alternator and at the connectors on the voltage regulator

Overall, your problem sounds exactly like the issue I have with my first car (and only non-volvo I've ever owned). My 1977 Datsun F10 Coupe (remember those?) had a very similar symptoms. Even with a brand-new alternator and voltage regulator, I couldn't keep the battery charged. The engine barely ran at full-idle and all-but died with any electrical system active. The car ran so badly that the catalytic convertor was glowing orange...

This problem made me insane for weeks, before I finally and quite accidently figured out that the votage regulator was not properly grounded. Cleaning up the connection and really getting the thing screwed down to the fender fixed everything.
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1967 P220 (My every-other-daily driver...), 1972 145S (1993-1997), 1973 1800ES (2006-Present), 1977 245 DL (1993-1999), 1983 245 (1998-2001), 1986 745 GLE (1997-2005), 1990 745 GL (2003-4), 1995 945 (2005-Present)....
What's a "Sedan"???