Did anyone notice that Moshe says, prophetically: your brothers will go to the war and you will sit here! Sit nashvu, from the shoresh yeshiva. So it is a clear mesorah from gedolim of Gad and Reuven!
If you look at pesukim carefully, there is a further remez: Moshe was the shepherd leading to his leadership in Torah, so are those who were heads of those yeshivas had a lot of sheep, clear remez to their followers, and they were even willing to put those sheep into protected spaces before their own children…