I've watched enough Let's Plays to know that it's a struggle to defeat Seymour's final challenge. Fear not! I've posted a video of me doing such a thing, along with instructions.
*NOTE: This is for the definitive version of Last Word, not the IGMC version.*
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If you've played the Seymour Challenges in Last Word, you might have found that Banter is one tough nut to crack. This is a strong example of how to defeat him.
I like to start with Subtle Disruptive, then linger on Power only long enough to blast that Overt Submissive. This is the most efficient way to grab Tact.
The key in the strategy is to get enough fuel to race out of the danger zone before Banter gets his own Tact. Once you use that Overt Submissive, you should have enough Tact to idle the Subtle Aggression to victory.
Notice that the focus is never to rely on harming Banter's Composure. If you can, yes, it's always good, but the main strategy is to build Tact quickly and then burn through it slowly.
If you follow the first first moves you'll find yourself in a good position against Banter. On rare occasions he'll press you into the spot left of the reddish peg, in which case you change your second phrase from Overt Disruptive to Common Disruptive.
He is built to work like a puzzle, but still has some wiggle room for his AI, so it's fair to note that near the end of the match he may choose slightly different phrases. Sometimes he can get you close to loss, at which point you can use Common or Overt Aggression to get out of the corner. This recording is a clean shot, though.
So long as you follow some basic principles of the setup and can adjust your moves a bit when needed, you can beat him every time!