Hmm, an interesting problem that I very much suspected was just the ignition switch.

One quick thing you can check with your car stuck at work is fuses. In your 240 there's a fused distribution block up by the battery. Follow the red battery + cable to a nearby rectangular plastic box. The number two "Y" fuse in that block supplies power to the ignition switch (pin 30). Start by checking that fuse and pulling it to see if there's any corrosion.

Putting in a new switch apparently made things worse? So possibly a Volvo switch that is DOA as you suggest, but I consider that unlikely. Is there any chance the new ignition switch wasn't seated properly or that a wire got pinched in between during installation that might be in the way. If the key can turn the barrel then the only way I can immagine the ignition switch not cooperating is if the half moon shaft that sticks out the back somehow isn't seated or the ignition lock got so damaged that it is no longer turning. You would need to pull the ignition switch off to confirm that. With the ignition switch off, you could then use a screwdriver to turn it to see if that makes a difference or even starts the engine. A better option of course would be doing some electrical diagnosis with a meter, but that will require a decent wiring diagram. If you didn't want to remove the cluster so you can get at the switch connector you could use the wiring diagram to find where these wires terminate elsewhere at more accessible spots.

Being that the car is stuck at work, another simple thing you can try is verifying the starter motor and battery connections. Along the left fender is an open spade remote starter connector that bypasses the ignition switch, either a single pink or blue wire, on a short lead from the main engine wiring harness. If you jump that to battery +12V the starter motor should crank. The car needs to be in Park so that the start inhibit switch on the shift lever assembly doesn't get in the way. If the starter motor doesn't click then short the starter solenoid terminals. If it now cranks then that implicates the start inhibit switch -they can definitely become a problem in their old age with dirty/worn contacts inside (you can attempt to open them for a cleaning).

Hot wiring a 1990 240 so that you can drive it is non-trivial, but it can be done. There are all kinds of things that need power plus interlocks and safety features that can get in the way -especially in automatics. You may want to refer to this old thread "How to start a 240 without a key? (in junkyard) 200" where Bruce Young explained the basic electrical bypasses for the ignition switch (many of us miss Bruce and his many contributions here)
https://www.brickboard.com/RWD/index.htm?id=1256435&show_all=1

Once Art gets onto this I'm sure he'll have more ideas after reviewing all your posts. I didn't have time here to rethink all your symptoms.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now