I have run Mage the Ascension in a variety of games, Mage exclusively or in crossover with other WoD games. I've had some two Seekings in the past, and recently three more, therefore I believe I'm qualified to give an answer. Unfortunately there is no short version of it.

Success and/or failure

It is a viable idea to ask the player to wager their XP on a roll - however I would say that when the roll is unsuccessful, the XP in question should be spent without limitation on Spheres, willpower and ability increases. Losing XP - and in this case probably majority of the pool - is frustrating. Avoid it. Players needs to shape their character. I am opposed to the idea of failing a whole Seeking because of an unlucky roll.

The preparation

The most successful of my Seekings were preceded by some core discussion between myself and the player about the future of the character. The most important issue and one that is often forgotten is that a Seeking changes the character fundamentally and irrevocably. This opening statement requires that the players agrees to substantially change his character's psyche, style, sometimes even rewrite the core concept. Have your player realise that they will have to choose (or have chosen for them) new Backgrounds for the character. They don't have to be completely disjoint from their previous ones, but different enough to show lateral character growth

When creating a new character I always make the player write down what holds the character back in terms of magickal development. Now is the time to use it.

• Take a look at their Nature - the primary strength and weakness of the chosen archetype is listed in the book. Note both of them. Do the same for Demeanor. You will challenge those during the Seeking.
• Consider character's Style. Do you see any limitation? E.g. one of my players used to derive her power from achieving an euphoric state. That limited her ability to do magic during moments of clarity and purposeful contemplation.
• Examine the foci and how the character uses it. The same character from above used dance to achieve euphoria. The Seeking showed that it was not the enjoyment that did the magick, but instead her momentary detachment from reality. The Focus can remain the same, but it's usage change or the other way around.
• Are there any other go-to strategies that the player uses? Tactics that your player instinctively does e.g. always run for cover in a fight, examine any unknown piece of technology before using it. Any preconceptions or strong beliefs? You might even go as far as to challenge your conservative friend to consider liberalism as a viable system.

Consider player's Avatar very carefully. Both will be extremely important, as a Seeking is Avatar's attempt to change the character.

The trial

The overarching flavour of the endeavour should be determined by Avatar's Essence. Seekings in it's truest form are delivered by Questing Avatars. Dynamic ones often tease the mage with randomness and unpredictability, while a Pattern one could delight in a series of puzzles or structured challenges. Primordial I find the hardest, but you could go wild, retelling the creation of the Tellurian or something similarly grandiose.

Try to make the Seeking plot relevant to their characters weaknesses. The journey should demonstrate that the character can overcome those flaws and the player abandon some concepts within the character. I recommend a series of challenges where playing within the scope of character's current style seems to be the most natural and intuitive approach but ends in failure. Now, don't be afraid to involve lateral thinking or paradoxical logic. This is Mage the Ascension! The player is aware that a Seeking is not about completing a quest, it's about doing it in a novel way, and if he's not, drop clues, as to what would be sufficient, in the form of visions or companions urging the character to "let go of his limitations".

Put the player in situations, where his usual tactics appear to be appropriate, but allow him to progress only if he chooses to do the opposite. E.g. if your character has Bravo Nature with Anger weakness, put him in a in a trash compactor. Springing to action (his default playstyle) is what the situation calls for (superficially). However, only if a character lets go of his urge to act heroically can he progress (trash compaction stops because it reacts to movement or sleeping monster's shell stops the compactor).

Every time such a challenge is completed, get your player to choose a new related character archetype. This will serve to show the transition and let the player retain control over the process. Once all of his limitations are overcome - he has a new Nature and Demeanor, player's go-to tactic had to be abandoned and new magickal style emerged, go to the finale.

Finish with a scene that enables the realisation that character's understanding of Magick was incomplete. Allow the player to come up with a new, improved version. Real-life example - one of my players used to do Magick by "hacking the server of the universe". The seeking made him wrong, and he decided that his new paradigm allows him to directly rewrite source code - going white hat.

Involving other players

I think you are right on the money. Talk to other players and plot with them against the Seeker. They should know what does the Avatar want from the Seeker and have a role to play - as enemy, friend or trying to lead him astray. They can even play as projections of their own characters (if they befriended the Seeker) or command more than one character. This should be their opportunity to play as something different. However, don't let them in on all the challenges, let them figure it out with the main player, but ask them to play double agents if they have better ideas than him.

To give some background to the creation of World of Darkness, the initial idea was put forth by Mark Rein-Hagen in a car trip with Stewart Wiek and Lisa Stevens:

While Rein-Hagen was on the road with Wieck and Stevens to GenCon 23 in 1990, he conceived of the game Vampire: The Masquerade which became his main project for the next year, and was published by the new company in 1991. Mage (1993) was based to a certain extent on a game that Rein-Hagen had imagined back in 1989 as something like a modern-day Ars Magica, although this was the first World of Darkness game in which he was not explicitly involved.

— Wikipedia on Mark Rein-Hagen, cited from the book 'Designers and Dragons'

While not a perfectly rounded quote, I have found a reference dropped at a panel talk uploaded in 2009 where it's said, of one of the panelists and writers of Mage (not the same author as WoD) while writing the rules,

He spent most of the time in this haze...

This sentence could be interpreted in a variety of ways and imply the writer(s) of this particular work were under the effect of a drug, overwork or sleep deprivation (or otherwise intoxicated). However, as noted below by @JackLesnie, there is a culture of 'mystic oracle' which is promoted around the development of White Wolf games.

It should be noted that much of the early written work for World of Darkness was written by a collaborative team of freelancers in an office at White Wolf - but the implication of Mage being a fever dream seems to be common among the writers.

I am confident that with another week of trawling through panel discussions one might find more references to the phenomenon - though my research leads me to believe this is an inside joke, an issue of overwork, a reference to the flavour of Mage and a running aura of mystique.

I've attained a response to my rather invasive tweet to Stewart Wieck. My question:

Could you settle a dispute? Was Mage:Ascension "written in a perpetual state of intoxication" or is it a comment on mechanics?

The response:

Only if a constant diet of Indian food is intoxication. Lots of solo dinners in Decatur, GA pouring over notes and ideas.

Re: mechanics, Storyteller was a given, but the wonky bits I did with it (Spheres, Avatar, Arete, Paradox) is all on me.

https://twitter.com/stewartwieck/status/701796775649103872

https://twitter.com/stewartwieck/status/701797600924545024