Nobody said the tribes of Israel were not active in 1200BC. The Merenptah Stele tells us they were active and identified at that point as a united people, Israel.
If the conquest was just beginning at that time, that would not be the case.
From this site:
Egyptian Domination of Canaan during Joshua/Judges.
I think there are good correlation for the destructions of the cities, and also for egypt, but there is an huge problem: if the exodus really occurred in 1500-1450 BC, the Israelites were present in Palestine between 1400 and 1200. But there are a lot of evidences proving that the Egyptians ruled the whole territory during this period of the time, and all the kings of Canaan (who were numerous and divided as it is reported in the Bible) were in fact nothing more than Egyptians vassals with a few autonomy.
You are quite correct that the Egyptians had political control of Canaan in 1400 BC and they maintained that control by means of suzerainty treaties with the kings of the local city states. The reality of the situation, however, was that the Egyptians had very few troops and other personnel in Canaan. They had several administrative centers in the lowlands, such as Gaza, Joppa, Megiddo and Beth Shan, but did not maintain a similar presence in the highlands. It was in the highlands that the Israelites settled, in the area that is often referred to as the central hill country. The areas that the Israelites could not conquer, listed in both Joshua and Judges 1, were the lowlands, the areas occupied by the Egyptians.
From this site:
joshua campaign map - Google Search
View attachment 83931
It seems to be the case that the book of Joshua had some bragging and exaggerration, but if Israel was not there in Canaan and then was there, it seems to be the case that Israel, as a people, conquered Canaan, not in a scorched earth way, but so they could live in most of the places that they conquered.
In Joshua and in Judges 1 we read of large areas of Canaan that had not been conquered, it was an ongoing thing as Joshua tells us.
It should not be a big problem to read parts of Joshua as bragging when the plain truth was, and which is told us, is that not all the people of Canaan were killed and that they lived there with Isael.