The last detail naturally reminded me of another semi-historical (or perhaps we should say demi-semi-historical) pair of outlaws from my own country's past, Robin Hood and Little John - who also met and became besties after fighting on a bridge. (Given Benkei's being a monk, we might also fold Friar Tuck into the mix.)
Is it possible that there was some mutual influence involved in the two sets of legends? I'd love to think so, but busy as the silk road no doubt was, there must be a limit to how much cultural transmission it could reasonably bear. And anyway, it soon occurred to me that these two pairs weren't unique. The grandaddies of Yoshitsune/Robin Hood and Benkei/Little John are surely Gilgamesh and Enkidu, the Sumerian odd couple who also began their friendship by fighting. Like Yoshitsune, Gilgamesh appears to have been a historical figure before he had a second career as an epic hero.
I wonder if there are other examples out there who fit the bill?