I had considered the 2nd Intermediate Period as the possible time of Exodus, but discarded it. Reason: I accept most of Joshua, Judges, Kings & Chronicles as historically accurate. I don’t always accept the Bible’s compilations of years as accurate. It’s pretty much undisputed that under the New Kingdom, Canaan was a province fully under Egyptian control. And Egypt exerted this control over quite a period. Yet, while the Bible mentions the conquests of Assyrians, Babylonians & Persians (all known historically through other sources) there is no biblical reference to Egyptian occupation.
Looking at the genealolgical timeline from Joshua through Kings/Chronicles, I see the greatest period of chaos in the Israelite conquest of Canaan, and then the rise of the kingdom of David & Solomon ~900-800 BC. Thereafter, Judea & Israel split, and the Assyrians assume ascendancy in the area. In the Bible, Assyrian King Sennarcharib refers to Egypt as a “broken reed,” which she surely wasn’t under the New Kingdom.
Thus, I put the Exodus at the 3rd Intermediate Period.
Another reason that I have tried to find reasonable explanations for the Exodus in the 1400s BC is that there are two dates in the Bible [and I hope maybe someone can tell me where, as I have forgotten] that indicate the Exodus was 400 and some years after the time of Abraham which was 18 to 1900 years BC, and 400 and some years before the Temple was built in Israel. Does anyone have those exact years, as well as the exact date for the Temple?