I'm of two minds.
One, people love a good tournament. It gives a chance for multiple match-ups, and longer-term storylines. Individual matches are also easier to write compared to a massive multi-man with multiple teams, so while there may be "more writing" the matches stand out more and you can tell a longer-running narrative with it.
On the other hand, it can be nice with the... massive massive delay to have the champions be crowned sooner. Then if you want a Women's title we can wait a couple shows since most female talent are mid-storyline right now then when the time is right, decide what to do to determine a Women's champion.
Let's see, the teams that won and qualified are...
Top-Gun (Maverick and McMichaels)
The High Command
The Residence (Slate and Nova)
Nothern Touch
and Brian/Humanity and the Crimson ghost.
Five teams is a touch awkward for an average match and yet a bit awkward for a full tag tournament. If we want it to be even, then The Bordeaux's, since kayfabe wise got screwed by a pre-match attack and the won the Tag Turmoil, you mentioned they can get themselves back in the hunt because of it, so if we add them to it, we can make things even. If we do that, then I have an idea:
This show, if The Bordeauxs are involved, we can have three matches determined "in kayfabe" by a random lottery. Living up to the name of the Lethal Lottery. The three winners, go on to a match at the next show to determine the tag team champions. That we can do as a specialty Triple Threat which I think a Ladder match is a fun idea.
Have the right person writing it, can be a chaotic and fun match, protecting the top teams by not having any of them be pinned. That way also, the tag team titles, if you want them on a somewhat even plain compared to the world title, can be the main event THAT show then the AMA Grand Title's first defense gets to main event Lethal Lockup. That way neither one, a first title defense and the crowning of an inaugural champion, doesn't overshadow each other on the same card.
