For BP multiplication, I've tried manipulating focus on characters by getting Echidna as low as possible, then creating a domino effect of one of the guards into her to get a 2x multiplier. While harder to pull off, especially with the targeting mechanics of The Bouncer, it could be considered easier than killing an enemy then trying to kill the boss immediately after.

The power stat definitely affects every move in the game, testing between G and S rank Sion, the basic punches, special moves and throws all have significant increases in damage. I've found Sion's triple high punch to be most effective with his move set in dealing the most damage in the shortest amount of time; an issue, however, is Echidna, mainly due to her having a smaller hitbox in defence mode, so it means the punches can occasionally miss.

Dogs and Kaldea work by doing the light-heavy combo with a low attack, but the issue, as you've pointed out, is that it seems to be difficult to gauge what is considered a hard button press.

Also I'm fairly certain the initial hit of a bouncing sequence is constant damage passed onto one another; thus, a far more powerful move that knocks an enemy into others is the key early on, but finding out what move does the most damage is necessary and what BP it requires.