Disclaimer: I don't own Naruto, all I own are the ideas my twisted mind can come up with. Naruto is owned by Kishimoto-sensei.
The Missing Hokage challenge: We all know how Tsunade only returns to Konoha because of Naruto. Well, in this case, the origin of this divergence is after the events at the VoTE, the Konoha village Council is upset over the mission's conclusion. The Council decides to go behind her back about Naruto so that they can banish him. Tsunade however, refuses to sit back and take it like a lost lamb. Her reasoning is that if they are throwing out the sole reason she returned to Konoha in the first place, she is going to leave with him.
Thereby, you have the premise of The Missing Hokage, as Tsunade decides to pack up and walk out of town with Naruto, Shizune, Tonton and Hinata all travelling along. But, she's also smart enough not to leave without first using the Hokage's stamp to her advantage. 'Team Hokage' as it soon comes to be known, are officially pardoned of all past crimes, released from all future obligations, and are walking out of Konoha with several notable treasures, including the Forbidden Seals scroll and a very sizable fraction of the Village's treasury. All released to Tsunade under her authority as Hokage, of course! If they want to treat her family like garbage, she can and will return the favor.
Things to happen in this challenge:
One: Tsunade has taken the hat with her.
Two: She takes both Naruto and Hinata on as her apprentices, after promoting both of them to the rank of Chunin on her authority as the Hokage. Naruto will go through some extreme chakra control exercises, but both Naruto and Hinata will start powering up, learning both her strength and medical techniques.
Three: Tsunade and Shizune will start studying from the Scroll of Forbidden Seals, and secrets from it are awarded to the two kids for successfully completing set portions of their medical training.
Four: The group goes through an extensive period of being wandering treasure hunters, like Indiana Jones, but ninja. They can move through any countries or encounter any characters I like while doing this. One preferred treasure hunt is to penetrate a certain castle and RETRIEVE, not destroy, the Lizard summoning contract held within.
Five: One of the items that they have in their possession is the Sarutobi's Monkey Summoning contract. Holding multiple summon contracts is possible, but most people have no reason to, most not even posessing enough chakra to summon one boss, let alone multiple.
Six: Because of their skill sets and treasures (both taken from Konoha and recovered on hunts), ALL Hidden Villages, both major and minor, are trying to get the Missing Hokage to settle down in their respective village. Some will use fair means, such as persuasion and incentives, others... will play dirty.
Seven: The Kitsune Clan bloodline from Chunin Exam Day, is available for Naruto and Hinata if you want to use it. That includes the regeneration, chakra boost, nearly prehensile tail and parabolic ears, although if you can find a way to add Wood or Ice you are welcome to them.
Eight: This should be a Naruto/Hinata matchup, though harems are also acceptable.
Back around town, the following should happen:
One: The Konoha villagers are very upset and for any number of reasons. The people, especially Team 7 (whether Sasuke was retrieved or not), who expected things to get better with Naruto gone are severely disappointed. If anything, the issues that they expected were going to improve with Naruto gone are getting worse.
Two: Without someone doing the paperwork, Konoha's infrastructure and mission assignments are now in a state of rapid degradation.
Three: In response to Number Two, the Village council that drove Tsunade away, eventually decides to revoke her title of Hokage for extreme dereliction of duty (this coming after her face is at least partially carved into the side of the monument). In Tsunade's place, they appoint Jiraiya, this time successfully getting him to accept the post.
Four: Jiraiya tries to get the Council to revoke their decree of banishment on Naruto, which they adamantly refuse. He points out that they have now directly opposed four of the six Hokage they've ever had on this issue. The Fourth wanted Naruto to be seen as a hero, the Third wanted him to be treated better, the Fifth had left town with him when they banished him and now Jiraiya, the Sixth, wants him back and they won't agree. When they still refuse, he performs an almost identical exit to Tsunade's, leaving town with a few Genin and loads of treasures to go join up with Tsunade. He also takes the newly-made, replacement hat with him.
Five: Soon after Jiraiya's departure, they appoint a Seventh Hokage: Kakashi.
Six: Although Kakashi stays in town, ALL of his bad habits as a Genin teacher continue to carry over to his tenure as the Hokage, and between his extreme lateness and laziness, having Kakashi as Hokage is no better than having no Hokage at all. The Village is in shambles, the clans are increasingly unhappy, and no missions can be done because the paperwork on everything is so far behind. Konoha is falling apart and some factions are becoming increasingly desperate to get one of their missing Hokage's back.
This is my response to Perfect Lionheart's Missing Hokage Challenge. I am going to use everything, except I am also going to add a twist. What my twist is, will be revealed later on...
Let's get started... with The Wandering Hokage!