In the short term it shouldnt be that hard to make it defensible, but the question is really one of long term security. This "meme" originated because I and others frequently see people suggest the pipe dream idea of Rome conquering and holding Mesopotamia as an AHC. The important point though, that I usually argue is more along the lines of "eventually it will fail" not "instantly the Romans will lose their gains."
In the time period I think you're interested in, pretty much no state held Mesopotamia without also holding Iran. Those that did were generally weak vassal regimes whose fortunes rose and fell based on the fortunes of whatever polity occupied the Iranian plateau. However, I don't think it's impossible. What you need however, has more to do with circumstance than state policy I think. Your best move is to figure out how to get all the seminomadic peoples living in the Zargos to support whatever invading power holds Mesopotamia. Give them a shared faith or similar culture or hell just have them be pissed at the Iranian state enough to collaborate with the invaders. The Zargos mountains simply aren't a geographic impediment on the scale of some of the others you've mentioned. Which is not to say they can't present a problem, just that they're not perfect. And Mesopotamia really is hard to defend. Has been since the dawn of time. Will pretty much always be.
The Sumerians, Babylonians and Assyrians all held Mesopotamia without also holding Iran, as later did the Abbasids, Ottomans and Iraqis. Given this, I'm not sure that the nobody-holds-Mesopotamia-without-Iran-in-this-time-period thing wasn't just a fluke.
One thing that always bugged me: How the heck was it always Mesopotamia catering to/being conquered by an Iran-based state, when it's Mesopotamia that's more fertile and (I think) more populous?
"This Artaÿctes who was crucified was the grandson of that Artembares who instructed the Persians in a design which they took from him and laid before Cyrus; this was its purport: “Seeing that Zeus grants lordship to the Persian people, and to you, Cyrus, among them, let us, after reducing Astyages, depart from the little and rugged land which we possess and occupy one that is better. There are many such lands on our borders, and many further distant. If we take one of these, we will all have more reasons for renown. It is only reasonable that a ruling people should act in this way, for when will we have a better opportunity than now, when we are lords of so many men and of all Asia?” Cyrus heard them, and found nothing to marvel at in their design; “Go ahead and do this,” he said; “but if you do so, be prepared no longer to be rulers but rather subjects. Soft lands breed soft men; wondrous fruits of the earth and valiant warriors grow not from the same soil.” The Persians now realized that Cyrus reasoned better than they, and they departed, choosing rather to be rulers on a barren mountainside than to dwell in tilled valleys and be slaves to others." (Herodotus 1.122)