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I assume you are installing the solenoid correctly, making sure the plunger is fully engaged with the pawl. If the solenoid comes out without twisting it you've done it wrong.
Now to figure out if the transmission needs to come apart. Can you move the pawl by sticking a small rod inside the hole where the solenoid goes? It should move a half inch or so and you should feel engagement.
There was a thread some months back where the reverse lockout rod was bent. This rod moves when shifting into reverse and keeps the pawl out of overdrive. When shifted out of reverse a flat spot on the rod lets the pawl move.
You appear to have done everything electrical and I think you may end up pulling this apart. The upside is you'll be an expert on how your overdrive workss.