One idea could be a time - travel plot. The Running Man characters could be sent back in time to the origin of the game show and have to compete in the very first, more primitive version of the challenges. Another idea is a crossover with other popular anime characters. They could team up or compete against characters from Naruto or One Piece, for example.
Saitama is a very powerful hero in the One Punch Man universe. He can defeat any opponent with just one punch. He has a simple appearance and a somewhat laid - back personality.
Sometimes King is paired with Saitama. King, known for his false reputation of being a super - strong gamer in the original story, could be in interesting interactions with Saitama in the fanfiction's gaming context. Maybe they compete in a gaming tournament within the fanfiction, and Saitama's effortless wins baffle King.
You can start by mixing the traits of existing Running Man characters. For example, take the physical strength of one character and combine it with the intelligence of another. Another way is to give them unique backstories. Maybe one character was a former circus performer, so they have acrobatic skills that come in handy during the challenges.
Genos could be an unexpected opponent. He might be forced to fight Saitama due to some mind - control or a misunderstanding in the rules of the tournament. It would be really interesting to see how Saitama would handle fighting his own disciple, and how Genos would fare against his master's incredible strength.
Well, Saitama All Fiction could potentially refer to a fan - created idea that emphasizes Saitama's ability to be above all the normal rules of the fictional One Punch Man universe. For example, his strength is so overwhelming that it's like he exists in a realm of his own, where the typical limitations of the story don't really apply to him. He can defeat any foe with just one punch, and this 'All Fiction' concept might be an attempt to explain how and why he's so powerful in such a ridiculous way.