I think that Persepolis not only should switch to an immortal I would go so far as to recommend that you whip it after 1 turn. I don't know if anyone realizes how dangerous the current situation is. 1900BC is right around the time when barbs start entering your territory (does anyone know the exact date for Monarch?). Pasargadae is defended by a single warrior and doesn't have the population to whip any additional defenders. If you wait until a barb unit appears at Pasargadae's border an immortal whipped in Persepolis wouldn't be able to reach Pasargadae in time. That would mean the warrior would have to defend and if it loses, well you know what that means. Say goodbye to your precious horse city (and your chances of winning?)

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I would position the immortal in the tile SE of the horses so it fogbusts that area while it's still in position to move to defend the city if a barb appears. Prior to finishing the barracks I would build two more immortals: a second immortal for Pasargadae (which should be fortified in the forest tile next to the city to deny the cover to any barbs that appear) and a garrison unit for Persepolis (you do realize your capital is undefended, right?). Then you can finish the barracks and start building your invasion force.
Pasargadae's build should be switched to a monument and a worker should be dispatched ASAP to chop the forest adjacent to the city (which will not only help complete the monument but remove that cover). The worker (with immortal protection) can then pre-build the roads needed for the corn and marble while waiting for the border expansion.
On a different subject I've been giving some thought to the timing of the attack on Qin and I'm wondering if it might be worthwhile to delay it a bit.
I'm sure this will be a bit controversial as everyone has been suggesting that the immortal rush needs to happen ASAP to catch Qin when he is weakest. But I wonder if this is really the best move. This goes back to the discussion earlier concerning using an early warrior to harass a neighbor and stifle development. At the time it was pointed out that that tactic is counter-productive when you're planning an early attack as you want your neighbor to develop their cities so that you'll get more when you capture them. With that in mind wouldn't it be worthwhile to wait a bit to attack Qin?
Now I'm not suggesting that you wait until there's a threat Qin would be getting LBs. But a short delay might be beneficial. Doesn't the AI focus more on infrastructure buildup (including workers) at this point? So Qin's defenses aren't likely to improve significantly for a while. Even if they do improve and some more immortals are lost wouldn't it be worth it if the captured cities are more valuable.
Qin doesn't have copper so there's no need to rush to avoid spears. And since Qin is Industrious if we give him some time how likely is it that he'll build a wonder or two that can be captured?
Writing next for OB would allow the early immortals to keep an eye on Qin's development and try to find an optimal time for the attack.
Of course a delay would be a bad move if the plan is to fight a second war with immortals. The problem in this case is that this map just doesn't lend itself to a second early war.