"Second, I seem to recall that a friend in your real life had said something that was making you question whether your compatibilism was valid."

Semantically valid, yes. Can a compatibilist say they made a choice or is the concept of choice so wedded to libertarian free will that the compatibilist's statement is a lie?

"The libertarian version is completely unworkable, as you say (though you didn't attach that name to it in your post). I assume that is what you meant by "four sided triangle"."

Correct.

"I had assumed your friend had scored a hit on this point. For me, what you describe is not free will because "[the agent] couldn't have chosen otherwise in exactly identical circumstances". Nothing free about that, IMHO. Though you appear to be saying I am remembering that conversation incorrectly since you indicate that you weren't questioning your position.

I'm not and wasn't questioning what happens when human beings make choices. I was questioning whether or not the general understanding of 'choice' or 'free will' includes the compatibilist conceptions. For 'free will', I think I can make a pretty good case because of the legal understanding of it. Legally a person can be deprived of their free will by coercion. But libertarian free will is unaffected by coercion - you have just as much libertarian free will with a gun pointed at your head as you do without it.