My position is that the Iliad is based on multiple events involving the Mycenaean Greeks (actually I hate the term "Mycenaean", so I will call them "Bronze Age Greeks" from now on). There are multiple mentions of "Ahhiyawan" raids in the Aegean and West Anatolia. The first one is Attarsiya who invaded and raided West Anatolia and Cyprus. Some have argued that Attarsiya is the basis for Atreus the King of Mycenae (the one who supplanted Eurystheus and the Perseids, he was also the father of Agamemnon), interestingly Atreus' grandfather Tantalus was said to have been Anatolian. The unnamed Great King of Ahhiyawa who was a contemporary of Muwatallis II and Ramesses II, mentions in one of his letters to the Hittite king that his own grandfather "Kagamunash" made an alliance with an Anatolian ruler (or Kagamush was the Anatolian ruler, and the Ahhiyawan ancestor is unnamed). Therefore the Great King of Ahhiyawa claims suzerainty over some islands in the Aegean which were given to Ahhiyawa by his Anatolia ancestor. This appears to coincide with the raids of Piyama Radu and his taking control of Lesbos. Presumably the islands disputed between the Hittites and the Ahhiyawans, around 1290 BC, were those islands around Lesbos. Piyama Radu is mentioned as having fled to the Ahhiyawans when the Hittites chased him out of Anatolia. This involves Wilusa because at the same time Alaksandu of Wilusa makes a treaty with the Hittites. Simultaneously the Hittite vassal king of Arzawa formed an anti-Hittite coalition and received support from the Ahhiyawans. Although Wilusa is an important piece, what I found more interesting is that Miletus (Millawanda) is attacked twice by the Hittites (in the reign of Mursili II and in the reign of his other son Hattusili II). Also interesting to note that Millawanda is claimed by the Ahhiyawans and its ruler Atpa pledges allegiance to Ahhiyawa.
The Arzawan ruler who rebelled against Muwatallis was also one of the architects of the revolt against his father Mursili II. Possibly also with some Ahhiyawan support in that time as well (about the 1310's?). Although the Ahhiyawans appear to have gone all in in the 1290's because not only are they mentioned directly fighting the Hittites, but the conflict involved Wilusa, Arzawa and all the lands in West Anatolia, presumably also fighting in the Aegean islands. Muwatallis II boasts that he defeated the Ahhiyawans, at the very least he defeated the Arzawan coalition and subjugated them. The Iliad mentions the powerful Memnon of Asia as being the key supporter of the Trojans. I can't help but think that Memnon is cultural memory of the Hittite Empire (although it seems to also be a reference to Ramesses II). The Iliad also mentions the conflicts against other Anatolian states, albeit mostly in passing, some of these states were allied to the Greeks. The only issue is that Wilusa is not mentioned as having been destroyed and peace is concluded some 30 years later when Hattusili II takes the throne of Hatti. In the treaty Millawanda is ceded to the Ahhiyawans and their king is recognized as "Great King", at least by the Hittites. Although their King is never mentioned in person, instead the king's brother Tawagalawa goes to Millawanda and negotiates the treaty. Tawagalawa seems to have been in charge of Ahhiyawan affairs in Anatolia. The Great King doesn't go to negotiate the treaty himself and the implication is that Ahhiyawa is too far away, so the only assumption is that it is all the way in Greece.
Only issues I am seeing... there is no mention of the destruction of Troy and the destruction of TroyVIIb isn't dated until the early 1100's BC. While a lot of statements made by Homer are corroborated (such as the Trojans worshiping Apollo, which the Wilusans did worship Appaliunas), the actual details of the Iliad are not supported. There is no mention of an Achilles or Odysseus, or even Menelaos or Agamenon. Alaksandu of Wilusa could be a reference to Paris (Alexander of Troy). But a battle hardened and self made king like Alaksandu hardly matches the description of the cowardly Paris. There is also no reference to a King Priam, closest match might be the notorious pirate from Lesbos (I hesitate to say Lesbian) Piyama Radu, but he is mentioned as having fled to Ahhiyawa when the Hittites defeated him. Some of the details are eerily similar though, the "Great King" of Ahhiyawa strikes me as too similar to Agamemnon's attempt to become a High King over the Greeks. Although the brother Tawagalawa is nothing like Menelaos of Sparta. I think the most egregious problem is that the Ahhiyawans do not appear to win this war. What is more it seems that, although Wilusa was important, the war centered around control of Millawanda, and the Ahhiyawans supporting the Arzawan coalition. Where as the Iliad makes it appear that this is primarily a war of the Greeks, and the Anatolians are just there to give support.
So presumably Ahhiyawa is not in Anatolia, seeing as that place has never been identified and according to their correspondence the Great King is unable to meet the Hittites in person. That means that Ahhiyawa has to be somewhere in the Aegean Sea, which is unlikely because none of these islands could support an actual empire... the only other candidate has to Mycenae. Although Mycenae did not actually rule all of Bronze Age Greece (hence why I say that the term Mycenaean Greece is misleading). It does appear that Mycenae had hegemony over the Peloponnese, maybe stretching as far as Attica, and they quite likely had control over the Aegean islands. The main reason that scholars tie Ahhiyawa to Bronze Age Greece, is because of the large quantities of Mycenaean wares discovered at Millawanda. That city being what we call Miletus and which is specifically mentioned by the Hittites as the place which the Ahhiyawans control. The Ahhiyawans cannot be the Miletans themselves, because Miletus was ruled by a governor or puppet king called Atpa. It is clear that Millawanda was part of an Ahhiyawan empire, an assertion which is supported by the fact that the Hittites were willing to cede Millawanda and recognize the Ahhiyawan ruler as a Great King. Surely the Ahhiyawans must have been somewhat formidable if they are not only recognized as a great power, but also that they were willing to fight the Hittites (by supporting the Luwians).
However early campaigns by Atarsiya look as though they were direct invasions of the Luwian states, and have much more emphasis on raiding. The Hittites did not have much control over West Anatolia in the 1400's BC. Once they chased out Atarsiya, they used these attacks as a pretext to establish their control and bring states over to their side. The text mentions a lot of double dealing between the Luwians and Atarsiya (for instance Madduwatta who flees to the Hittites, they give him a new kingdom, and then Madduwatta rebels against the Hittites with the help of Atarsiya who chased him out). Atarsiya's attempt was likely an earlier expedition to establish some kind of foothold in Anatolia. Although it is not clear if Atarsiya was a king in Ahhiyawa (as the text only refers to him as a man of Ahhiyawa) so we can't know if he was doing this of his own accord (as a sort of viking) or if he went on behalf of the Ahhiyawan authority. At the very least we can be sure that Ahhiyawan raids were a frequent occurrence, as were Anatolian raids. Such that it is not surprising if there existed sufficient material with which to string together a narrative in the form of a great epic. Since the Iliad contains anachronisms (names of peoples, place names, weaponry which appears to be from earlier in the Bronze Age) I think that it makes sense to conclude that the Iliad contains multiple events and that are woven together into a single story, an exaggerated story most likely. Now did the Greeks come back in the 1100's BC to burn down Troy? Possibly, although the state of affairs in Greece was likely one of civil war, so I am unsure how the Greeks were able to invade Anatolia again. Perhaps Troy VIIb was sacked by the Sea People (mostly Anatolian Luwians).