if we stick to the bible we cant go wrong .Ok. So we have in common with the "1656-year" interval. Just not when it all began.
As I have said, 18th dynasty of Egypt had control over the whole region at this time - Canaan, Sinai, Moab, Edom, Syria etc.
Also Joshua would have invaded Canaan, shortly after 1473 BCE. This would have been in the reign of Hatshepsut (1479-1458 BC) and her stepson Thutmose III (14791426 BC), and Egypt was at one of its peaks in its empire. Joshua couldn't not have taken Egypt at this time. Thutmose was one of Egypt's greatest empire-builders.
Egyot and the Mitanni (in Syria) were fighting over the control of Canaan/Palestine at this time. Thutmose III had succeeded in forcing the Mitanni empire to surrender to him. Do you seriously think he would have not easily crush Joshua and taken back Canaan?
Egypt briefly lost control of Canaan during and after Amenhotep IV or Akhenaton (13531336 BC), but Seti I (129079 BC) and Ramses II (12791213 BC) won back Canaan.
If you believe that Exodus happened around this time (1513), then the Israelites' twelve tribes would have being serving as province for Egypt in Joshua's time. Again, I will say that your dating is far too early for the Exodus and Joshua's invasion of Canaan to happen because of other events outside of the Biblical events.
All Scripture is inspired of God and beneficial for teaching, for reproving, for setting things straight, for disciplining in righteousness, that the man of God may be fully competent, completely equipped for every good work.2 timothy 3;16