Greetings from Solveig! To some extent I think that we are
interpreting "battle cries" differently. My general impression of
people in the Society is that when they are looking for battle cries
they are looking for something to personally shout during combat.
Now then. Unit commands are another matter. I didn't have the
impression that the original questioner was a unit commander.
Actually, there are several different contexts in which short phrases
might be encountered: commands, call and response, cheering,
individual utterances during combat, &c. I don't know how much general
interest there would be, but it might be interesting to put together a
basic guide to Japanese martial speak.
As for the H's -- I remember hearing them in the movie maybe you
don't. And yes EI is standard romaji for "AY" as in "HAY". I don't
know how up on Japanese transliteration the particular questioner was.
Note to everyone. N is the only consonant which can occur at the end
of anything Japanese.
Your Humble Servant