If I can put down my opinion about the two options, just an input:
1) doesn't necessarily have an extreme advantage for the first player, you have to take in account that the second one has the final saying in the movement of mirrors and of the players (but I think you already know that), even though the first has the advantage in the shooting phase. I also think that in this case an Initiative stat make sense because you can say that the advantage of the first player is offset by the disadvantage in having lower stats in other places, so...yeah...it is something that needs to be thought about properly, but I think it can be managed without longer battles.
2) I don't know if simultaneous play would improve the game, maybe more balanced in terms of turn order but would also move the game more in a "read your opponent" territory and less on the "solve a puzzle turn by turn" territory, which is absolutely fine but personally, as a fan of more euro-style board games, I would prefer the second "territory".