The first possible date is (concordant with the literal biblical date of 1446 BC) during the second half of the fifteenth century BC (see here, p. 169, for the store city of Pithom and here, p. 29, for the store city of Ramses). The only difficulty with the literal biblical date is the complete absence of Egyptian mentions of Israel in the fourteenth and first half of the thirteenth centuries BC, even in the copious Amarna archives.
The second possible date is in the second half of the 13th century BC, say, between 1250 (so far back just in case the 40 years in the wilderness was literal) and 1209 BC (the date of the famous Israel stele of Merenptah). It cannot be early in the reign of Ramesses II, for the obvious reason that the main phases at Qantir/Ramses (some 300K people) and Tell el-Retaba/Pithom date to his time and Moses is said in the Bible to be 80 years old during the time of the Exodus -if the Pharaoh of the Oppression was Horemheb (or, if the Pharaoh of the Exodus was Merenptah, even Seti I) and the Pharaoh of Moses’s fleeing was either Seti I (in case Ramesses II was Pharaoh of the Exodus) or Ramesses II (in case Merenptah was Pharaoh of the Exodus), this would imply the Pharaoh of the Exodus was either Ramesses II (in case Horemheb was the Pharaoh of the oppression) or Merenptah (in case Ramesses II was the Pharaoh of Moses’s fleeing).
If Moses’s literal age was intended by the biblical authors to be 80 when the Exodus occured, the Exodus would have to have been intended to date either c. 1226-1213 BC (if Horemheb was the Pharaoh of the oppression) or the oppression would have to have begun very soon after the famous Hyksos expulsion in the mid-sixteenth century BC (which fits the background of Exodus 1 very well).
Good work.