One idea I had was to mix up a lot of the existing categories. I think the team leaders had the perfect mix of challenges for the category. Some other ideas might include:
Marksman (I think the category was actually called "projectiles"):
Archery competition, quick-draw fight a la the old west, target competition with their weapon of choice, weapon swap (they get their opponent's weapon), sniper off (they start far away/have to hit targets that are very far away), clear a room of goons (they have to take out a room full of, say, 2 dozen regular enemies as fast as possible), headshots only (a regular fight that can only be ended with a clear headshot), island fight (they are on two separate islands that are a hundred meters apart and cannot cross over to the other's island. They have a tree for cover).
This is the category that could use the most overhaul in my eyes. Don't get me wrong, characters like Lelouch are very smart and strong contenders, but they're not "mad scientists" or "evil geniuses" in my eyes. They're moreso strategists. Some ideas to refocus this category include:
1-day prep (each combatant has basic knowledge of the other, and a lab of equipment with 1 day to work on it), target (character) (both combatants have the same target. Who takes them out faster? Examples include Superman, Batman, Captain America, Silver Surfer, etc. Characters of various power levels), Prison escape (both are thrown in prison, who makes it out first?), fully equipped (each combatant gets any equipment, weapons, and minions they canonically have. Who wins?), fix climate change (both set their minds to fixing climate change. Who can do it faster/better?), advance humanity (each has 1 year and access to as many scientists, resources, etc. they could want. Who can advance science further?).
Stuff like this would allow characters who previously fit the category, but got outshined by physically superior competition, to have their time in the sun.
Just a few for this one:
Work the crowd (they're putting on competing magic shows. Who can win over the audience?),
A big pitfall of this one, in my eyes, was that it ultimately still boiled down to "who can hit harder?" Some scenarios to fix that:
Scare off (the characters are given Monster's inc doors and told to scare as many people as possible in 1 night), Creature Feature (the two face off against each other in a movie-setting, but rather than simply having to kill a certain target they actually get to fight), Scare (character) (without killing the target character, who can get them to voluntarily leave their house/run away first?), Monster hunter (a famous monster hunter is after them. Who survives the longest/takes out the monster hunter first?)