>on the left, I had to keep reminding myself that the actions on the right were mine (even though my character is standing on the left of the screen).
A fair perspective. The move history (like the move predictions) is ordered as action->reaction, and they're color-coded as well (red for opponents, green for player, gold for whoever happens to be champion). The player being on the left is just a general convention (see in particular most 2D fighting games). I hadn't really considered that the positions clash somewhat.