I'm fairly convinced that we cannot win this competition without resorting to some form of sabotage or other action (or lack thereof) that inconsistent with our goals. The "Potion of Fading" seems to be our best chance, but I doubt that will be enough considering our competition.
Speaking of which:
alfheimwanderer, are we locked into the "Potion of Fading" or can we still make one of the others from the "Potions Discussion"? Barring that, could we acquirere a different one by helping someone (e.g. Lestrange, as an alchemist, seems to be a match for the "Potion of Restoration")?
Accepting that we won't win, the main question that arises is: What do we want to get out of this championship?
We want to survive without debilitating injury, not embarrass ourselves, boost friendship/affection/reputation, and hopefully learn how to make a useful potion or acquire one from a collaborator.
Therefore, our best option seems to be allying with someone we want to win and developing the abilities that are useful to this end. The greatest synergy would be pairing with someone strong in potionmaking, but comparatively weaker in scavenging.
Maybe I'm misjudging or missing things, so everyone should feel free to argue against my perspective and I'll change my voting preferences accordingly. Otherwise, I'm going to try to maximize support abilities (ingredients/herbology, survival, navigation, etc.) to get, at best, second place. It would also be optimal if we could decide which partner we want as soon as possible.
Choice 250:
[X] The Catalog of Ingredients
Shinji (and Budge), assuming Zelkova can borrow Shinji's knowledge of ingredients (how else did he know English ingredients?). If not, then Zelkova should definitely read this as he is best at searching for things.
[X] Partial write-in
Spend 10-15 minutes skimming through maps to note any obvious dangerous areas (lots of path endpoints or areas that are avoided).
The rest of the time: Journals / Records left by past Champions
Prioritize the most recent participants such as Yumi and the Mahoutokoro survivor, then survivors of the second to last contest, then Mahoutokoro participants beyond that. I don't know how much time this would take, so only go back 50 years at most and use any remaining time on the investigation reports.