This has been explored most recently in Nadav Na'aman's article "The Exodus Story: Between Historical Memory and Historiographical Composition."

I indeed found elements of this article persuasive; and I think /u/Flubb's comments in this thread sync up with this nicely (at least some of the more general arguments of Na'aman). That is, Na'aman emphasizes that

Scholars’ conclusion that the Exodus tradition is mainly myth devoid of historical foundation does not take into account the antiquity of the tradition, its centrality in the historical memory of the Northern Kingdom and its central place in biblical historiography from the seventh century BCE onward. It is reasonable to suggest that such a fundamental claim of establishment would have emerged from a particular historical experience. Most likely, we should assume that it is rooted in a highly memorable past event of the people of Israel or at least some of them.

More specifically speaking, Na'aman indeed suggests that "the major event underlying the Exodus tradition is the dramatic Egyptian withdrawal from Canaan after the Egyptian bondage reached its peak during the Twentieth Dynasty."

Naturally, this proposal would entail a lot of role-reversal and garbled memory (which Na'aman goes into at some length, discussing the possible trajectory here). But I think we do have to account the magnitude of what seems to be the impression left in Israelite memory -- yet bearing in mind the logical/historical problems with the traditional account.

Forgive me that a lot of this has been rewriting my comment here, but... Na'aman also notes that

Canaanite rulers . . . sent slaves to the Pharaoh as part of their regular tribute or as a gift. For example, the king of Gezer sent 46 maidservants, five attendants and five guards, and the king of Jerusalem sent ten slaves, 21 young women and 80 prisoners.

Perhaps -- if we are to see the exodus tradition developing due to Egyptian activity in Canaan -- there's some element of this tribute that played into the notion of Israel's subjugation in Egypt... but, still, the idea is that the bulk of the oppression is being felt more-or-less locally.

But there's also an element of genuine "foreignness" (or... externality?) to his proposal. In the /r/AskHistorians thread I already linked to, /u/Flubb reiterates that "Israel always came out of Egypt in the earliest [Biblical] texts." Na'aman also suggests that

Another element that might be connected to the shifting of memory from Canaan to Egypt is the tradition of YHWH’s origin from the southern periphery of Canaan. This is evident from the Song of Deborah (Judg 5:4–5), the Blessing of Moses (Deut 33:2) and the prophecy of Habakkuk (3:3a).

. . .

According to all these sources, YHWH, the divine leader of the Exodus story, originated from the southern periphery of the settled country (Seir, Sinai, Paran, Teman, Midian), an origin that fits well with the historical memory of Egypt.

(Interestingly, it's also the Midianites who sold Joseph into slavery in the first place, leading into the events of the exodus [at least narratively/canonically-speaking].)

That being said, though, you might also want to look into /u/Flubb's comment(s) here.