So the Persians were interested in staying active in Greek politics insofar as they could keep the Greeks fighting one another. Presumably they backed Lysander to weaken Athens and maintain the Greek balance of power?
Well, they back the Spartans in two phases, really. Previous to Lysander's alliance with Cyrus, there was a weaker affiliation with Tissaphernes and other satraps. However, as of about 412, Darius II had issued instructions to back Athens, but Alcibiades managed to convince Tissaphernes that favoring Sparta completely did not support a balance of power (because it left Sparta pre-emenient)...and of course that it would be better to prey upon Tissaphernes' rival, Pharnabazus. I suspect Tissaphernes may have been more motivated by the later (i.e. greed), but the former point is not without merit: after the Sicilian Expedition, the Oligarchic Revoltution of 411, and the widespread revolt of Ionia in 412, Athens is on the ropes. The constant naval campains between 411 and 404 pretty well demonstrate that the two were evenly matched; hence, if the Persians overly favored either power, they would themselves upset a balance of power.
If the Spartans were to lose this battle in 404, then would they then intervene in the Persian civil war?
Good question. I think so. I do not think the battle would have itself been pivotal: it does not eliminate Cyrus' finances and it does not re-conquer Ionia for Athens. Furthermore, Lysander's (and Sparta's) reliance on Cyrus only increases, if they still want to fight Athens. What may happen, however, is that Lysander's loss (or lack of victory) turns opinion against him in Sparta such that when the Spartans learn of his meddling, both with Cyrus against Perisa and in the interal affairs of the Ionian cities, they may act to undercut his authority, further complicating things. The Spartans also don't have to outright support Cyrus for a Persain civil war to impact the fighting: if Lysander decides not to help Cyrus recruit Greek mercenaries, then perhaps Alcibiades might do so instead (or intriuge with Tissaphernes to prevent Cyrus' action). The best bet for Athens may be the latter, since this would leave Artaxerxes in Athens' debt and perhaps get the Persians to stop supporting Sparta.
By the political situation being altered, you mean Alcibiades is allowed to come back from exile after playing a pivotal role in an important Athenian victory?
By 404, Alcibiades is only in exile because he "chooses" to be. Alcibiades had left after the Battle of Notium if 406 (just before the victory at Arginusae), in which the Spartans decimated the Athenian navy (largely because of the incompotence of Alcibiades' lieutenant), necessitating radical measures (freeing slaves for rowers) to raise a new fleet. Alcibiades was not exiled as a punishment, he simply didn't go home. Most likely, he kept away because he had only returned when he had been able to deliver victories (and thus keep his enemies from trying to prosecute him and thus condemn him to die). After a victory that's pretty much his fault, the same logic dictates staying away. Hence, this would be the second time Alcibiades had returned from ignominy. The political ramifactions are two-fold: first, the change in sentiment at Athens about Alcibiades (do they still love him or can they see through the hype?) and the factional ambitions of the commanders making the gesture. Unfortunately, I can't remember who was at Aegospotamai to be making the gesture and Wikipedia doesn't say, but it will greatly affect the fortunes of Theramenes and Thrasybulus who are on their way to being influential (though things have been greatly muddled by the trial of the generals and the revolt of 411). The remaining oligarchs may be even more suspiscous of Alcibiades after the generals' trial, but so too may the people at large be looking for any kind of preeminent leader.
So Lysander loses the fleet, then the Spartans' ally Cyrus loses his bid for the Persian throne. I think that is a recipe for this return to power of the traditionalists. It would appear that the Athenians are in bad straits, and would jump at the chance of a light peace, and from the sound of your post the lightest peace they could get with Sparta would be with these traditionalists in power. Is that correct?
Yes. The Athenians are hard-pressed; how hard-pressed is hard to say, since Athens seems to be fairly resilient, but even the most die-hard pro-Athenian admits that things were tough in 404. It's the equivalent of France asking Germany for a negotiated settlement in 1918, the day before the Germans are about to do likewise. They could probably stand to fight on a few more years, depending on what their opponents are doing against them.
And here is where the Persians can re-insert themselves into Greek politics. So in the wake of Sparta abandoning the anti-Athens coalition, Corinth and Thebes form their own league to oppose the Athenians. This league seeks and gets support from the Persians, who having lost their Spartan counter-weight to the Athenians, view the C&T League as the new counterweight for Athens.
That's actually a possibility I hadn't considered, but it is could easily happen. It might be difficult for Thebes and Corinth to continue the Peloponnesian War itself. I'd expect that they refuse to recognize the peace, then organize a League, and then make overtures to Persia. This might result in a war around 395 or so, which would make a parallel of OTL's Corinithian War (Persia supporting Athens, Corinth, Thebes, and Argos, against Sparta).
Perhaps following the victory in 404, and then with the Persian civil war on going, the Athenians are able to strengthen their position in Ionia and retake Amphipolis? They don't want to expand to quickly or seem to recover too much however, because then that would probably tip the political balance in Sparta and bring the anti-Athens leaders back into power. Would this less-pressed Athens be able to hold off Corinth and Thebes?
I agree that some restraint will be needed. This is why I suggest some kind of Bill of Rights for the allies. It seems to have worked later on OTL in the fourth century, so maybe it allays some fears here. Retaking Ionia and Amphipolis is a lot for Athens to manage in 404. I'd expect that Ionia is independent, under terms of autonomy similar to OTL's King Peace of 386. The Aegean states are Athens' allies but with new guarantees and a new structure for the alliance. Amphipolis won't be easy to take, but it's not impossible. Another priority may be fortifications around Attica to prevent another Decelea (the fort Agis built in Attica to contiunously raid the countryside); OTL at some point in the 4th Century Athens built a fairly extensive network of such outposts. Since Athens keeps its fleet and its walls, it's in pretty good shape, regardless.
The outcome of the *Corinthian War depends on many things. First, does Athens have Amphipolis or is constantly diverting resources to try and take it? Next, is Argos a beligerent? OTL Argos joined the Corinithian war against Sparta and did fairly well. If Argos fights on Athens' side, then Sparta may begin to get nervous: Argos borders Laconia itself, though protected by mountains IIRC. However, Athenian cooperation with Argos itself doesn't necessarily provoke aggression if the traditionalists at Sparta are strong. I'd expect the events which force Sparta's pull out to leave the traditionalists in power, with a few rampant hawks. The combination, however, only leads to expeditions against Sparta's nearest neighbors, particularly Mantinea, Tegea, and other Arcadia (those most accessible to it and on which its security most depends). The degree of Sparta's isolation is thus a crucial factor. Lastly, what is the status of Megara (between Corinth, Thebes and Athens)? Megara may be declared autonomous, like the Ionian cities; it seems to have been neutral OTL in the Corinthian War. If so, all sorts of armies will be marching through it. This may be the issue that starts the war (not unlike the first Peloponnesian War in the 460s/50s).
All told, I could see Sparta's actions against her northern neighbors beginning to pull it into the war, but perhaps
on the Athenian side! Sparta has few real quarrels with Athens if her prestige does not depend on protecting Thebes and Corinth. Indeed, hawks may want to punish the two upstarts for betraying the Peloponnesian League. All-out alliance with Athens may be bit much (
may, remember the alliance of 421 happened even after the Archidamnian War). Corinth seems to have ripe for revolution in the 390s, probably due to the economic exigencies of decades of warfare and of Athenian attacks on her commerce. OTL, Corinth's narrow oligarchy fell to be replaced by a radical democracy and then formed an union with Argos (or Argive democrats tried to seize Corinth, depending on your take on events). Thebes will be the tough nut to crack, since it has immense infantry potential; the problem is that this wasn't realized until much later and under much more radical leaders than will be leading the Boeotian Confederacy.
If Sparta can be kept out of the conflict, then Athens' odds are pretty good. Yes, Persia's support is potentially huge, but OTL the support was pretty light (compared say to 470). I'd guess that Persia will build Corinth a fleet like it did Athens OTL. This fleet might be dangerous since Corinth may have the help of Syracuse, who seems to have pioneered new forms of triremes in the end of the Peloponnesian War. However, Syracuse will probably neutralized by tensions with Carthage in Sicily. The naval contest may give Athens a chance to re-tool, however, and re-prove its supremacy. Athens commanders are probably Alcibiades and Thrasybulus. It makes most sense for Alcibiades to be sent off to Amphipolis or to talk with the Persians while Thrasybulus does most of the fighting. If so, Athens probably wins: OTL, Thrasybulus managed to conquer most of Athens' old empire between 391 and 388. With more resources and with more strategic assets intact (Long Walls), it's only easier for him to do so.