Not at all.
The war bugle is intended to have a fixed base damage like bows and bowguns. I don't have their rules in front of me, but I think some of their special moves scale with Melody.
Yes, special attacks without listed Harm use the weapon's current Edge value. Also, Edge gets spent after the attack (to avoid the situation your wife describes).
I'd probably forego the Tempo Change if the monster was stunned, unless the scavengers were in need of a more challenging fight. In that case, I'd just pick something to intrude upon the Bout.