I downloaded the 425 AD save. Let's analyze where the OP is going rather than where the OP has been.
The primary goal in this game is Diplomatic Victory through the United Nations. We know that the restrictions of the OP ensure Montezuma will never be eligible for this victory unless he builds the UN; thus, it is imperative we get to Mass Media first and build the UN before anyone else can. Now, although the AI suffers from having a lack of land to develop (making this map type a much better one for the OP's restrictions than, say, Inland Sea), it will still build more cities than Montezuma, have more wonders than Montezuma, and have more production bonuses than Montezuma. Furthermore, there are two AI on this map - Pacal and Willem - whom I've seen throw themselves with gusto into rapidly teching Radio and Mass Media for the modern wonders. Thus, I don't think the main problem right now is Alexander or avoiding a DOW; I think the main problem is securing the UN. The diplomatic relations won't even matter if Montezuma can't get a seat at the table.
So, how will we get there?
Only Sitting Bull and Peter are lacking Literature, one of the potential trade chips a player can use along with Aesthetics to try and climb back to tech parity. Presumably, at least one of the AIs who have Literature are also going after Music to build The Sistine Chapel; while they won't trade that tech until the wonder is finished, we likely cannot make it to Music in time to get much value from it.
If we concede that we can't get The Great Library or Sistine in time, then Literature or Music may not be of much use for us to self-tech. Instead, we could pursue Drama, hoping the AI neglects it (as I believe it often does). Our capital won't get another great person in time to bulb, say, Philosophy, so we can't rely on a trade chip there. Our Great Engineer can bulb Metal Casting, but only Sitting Bull and Peter are lacking it, so we will not gain much value by doing so. Despite having the Pyramids and running Representation, we're not currently able to run many Scientist specialists, so we're mostly relying on our commerce to propel our tech rate. Presuming our situation does not change relative to the other AI, we will not be the first to Mass Media. We won't even be close.
Is it reasonable to conclude we must now try for a Cultural Victory instead of winning the UN? If so, then we can change our priorities.
Offhand, Pacal is plotting war.
Likely, Pacal is targeting either Alexander or Kublai Khan, but it is possible Pacal will declare war on anyone but Peter (they haven't met). I don't think we should worry about a DOW - we need our hammers for other things, it's unlikely that Pacal will DOW on us, and, if he does, then that's probably "good game."
Continuing on-topic, if we now attempt to prepare for a Cultural Victory, then we can actually make use of our Great Engineer. While we could use him to rush-build TGL, a stronger play may be to research Music and use the GE to rush-build Sistine. This will serve two purposes: #1) Denying Sistine to a culture-pursuing AI like Pacal or Willem. #2) Making a Cultural Victory easier for us. Unfortunately, we lack religion in either Clamcorn or Dyelake, so we're going to have to hope auto-spread saves the day. Furthermore, assuming we only get three cities, we'll be limited to just one Cathedral per religion. Still, Sistine (and thus Music) would be of considerable use.
Speaking of culture, if we had the Espionage Points, then we could take advantage of Yekaterinburg's placement to steal some techs from Peter.
Anyway, I don't think this game is hopeless. Sure, the UN seems a bit out of reach, but it's possible we could secure a Cultural Victory before any of the AIs win Culture or Space. We might not be able to slow down the AI through self-DOW, but, hey, the situation could be worse. We could be Toku, and Peter could be Monty.
Now, briefly springboarding off-topic, regarding the OP's lack of desire to finish this game on the forum (or at least not in this section of the forum)... I think enough people have consistently proven their interest in the Immortal Minimalism series, especially after this query had been brought up in
Immortal Minimalism, Chapter III - Augustus Caesar, to showcase why that shouldn't be true.