[X] Enforce strict time limits. Everyone shifts phases after about a half a week, whether they like it or not. People who are done, people who are waiting, people who are mid roleplay. All switch over.
[X] Allow applications for both Masters and Servants. Look, let's be frank. You're a god amongst men when you compare yourself to the other people who GM on this site. You think their failings will apply to you? Psh, you can run with PCs as both halves nooooo problem.
[X] A moderate number. You can probably handle like, half the bracket, right? Or about that? You'll probably have to mix in some NPC fights for people to beat up on while they wait for the PCs to advance.
[X] Only allow applications for Masters. Look, let's be honest. People can't write Servant sheets for shit. They're always overpowered, unbalanced, and a pain in the ass to boot. You'll have them run the Masters alone, and assign them a set of Servants you've made yourself.
[X] Let people move at their own pace. This is what basically every other game does, and often things get bogged down in the first Night phase as people blow their loads everywhere and run out of energy. Since it's an Extra grail war, though, the phases will work a bit differently, with enforced downtime and only one-on-one combat, so maybe that'll help?
[X] Everyone is a PC. You may be clinically insane. Every single member of the tournament will be represented by PCs. You're not sure you can do that, but if you do you'll be a legend.
[X] A small number. Keep it manageable. You can make a big chunk of the tourney NPC operated, keeping it just to PC vs PC fights in a single part of the bracket. Probably the easiest to do.