Ah, you may be correct about rounds vs turns. I am by no means a seasoned wargamer - I may be getting the convention wrong! I've jumped in the deep end despite minimal recent experience.
I was thinking of boxing - you take turns hitting each other (effectively) for a while, then the "round" ends, and then you start over.
Yes, I agree about symmetry. I did it this way to save myself having to playtest as much :p - the next/bigger version is very asymmetrical, a kind of clifftop scifi Dday landing scenario.