I agree with your characterizations of Alex's "ways out" of arguments he cannot win (after witnessing his style for so long, how could someone not agree?). But don't let it get to you.
I think you elevate his field of expertise to something that makes his obtuseness and stubborness a justifiable inconvenience of his brand of 'valid' criticism. Fine, if he criticizes others with equal expertise. I mean, while it's one thing for a high school kid to call you a twerp, it's another to have a PhD-equivalent call you a twerp.
Instead of perceiving a PhD-equivalent's admonishment as an admonishment of PhD-esque proportions, in this case we should remind ourselves that only a PhD with some severely diminished sense of self could be so petty.
The reason Alex reacts to many ideas with the pettiness that he does is because in our expressions of these ideas we reveal that which he lacks. For instance, the argument for a temporal dimension requires just a bit of right-brain imagination. That he rejects Einstein et al is not proof that he knows something the relativists do not; it reveals his anger over his inability to "get it." Add to that the fact that many people who do "get it" are not (at least do not advertise themselves as) science-related PhD's, and we've got one bitter, petty character on our hands.
To make a simple and exaggerated parallel, if you're homeless, and you see a quarter on the sidewalk, you might want to walk over to it and pick it up. But, if a rich man stops in his Jaguar, runs over to you, and begins fighting with you over that quarter, you should know that there is more value to that quarter than 25 cents. Further, if you were to somehow get the quarter before he does, any belittling by him of the "measly" quarter you've found would reveal that there is something about this quarter the rich man covets.