Sounds like you already got the best advice for the problem, but I'm curious if you tried the solenoid-bridge trick. It's a bad thing to do for more thana test as you run the risk of killing your solenoid. But...

You can bridge the two contacts on the solenoid with a well insulated scredriver. This will bypass the ignition switch. If will crank a bit if there is current available. It's a good way to eliminate certain systems from the list of potential problems. My old volvo mechanic also used this trick with a remote starter switch when to easily adjust the gap on my '72 145's lifters.

Also, I think someone already mentioned this, but I'll reiterate my own possibly relevant expereience...

Your problem sounds familiar to the first problem I had with my '76 240. The safety switch in the automatic shifter was not making good contact. No matter what I tried, the car would not crank. I even pulled the started and had it tested. Eventually a friend randomly pushed and held the automatic shift lever a bit to the passenger side (making the necesary contact), and as if my magic, suddenly the car cranked.

It's something you should try before you delve into any of the relays, solenoid test, or wiring.
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1967 P220 (My every-other-daily driver...), 1971 P1800 (The Parts Car), 1972 145S (1993-1997), 1977 245 DL (1993-1999), 1983 245 (1998-2001), 1986 745 GLE (1997-2005), 1990 745 GL (2003-4), 1995 945 (2005-Present)....