As an adjustment, may I suggest that the 2nd round only gets GUARANTEED first strikes, and third+ round gets none? Getting rid of it alltogether past the first attack is a bit harsh, and wouldn't be obvious at all to the player.
EDIT: As an alternative, maybe you could limit FS to once per combat, up to the FS number per turn. So a unit with 2-3 First Strikes would have guaranteed 1 First Strike for the first two fights, has to roll on the 3rd and never gets a 4th. This may also help balance out first strikes as they are.
That's what I meant really. That is to say, if not all first strikes are used up before it wins its first fight, then any that weren't would be left over for it's next one (and so on).
However, I'm going to leave it be for now, and wait for TB's more comprehensive rework in that area.