I originally tried to convey Nanase's puzzle game performance with dialogue, but that wound up being a bit confusing and wordy given the number of "Nanases" involved. A Nanase leaderboard visual was much simpler.
Boring Two-Player Mode
The fact that single player can be compared to two-player does suggest a rather boring two-player mode in which neither player affects the other. I propose the head canon that it is an unpopular optional mode, and that two-player modes exist in which you can do a thing, and it will affect your opponent in some way.
Intern Fox
I decided to go with what is effectively a joke instead of try to think of something for Fox that's not already in use by something else.
That's specific to Fox, however, and there may be a better, more general way of putting the concept of giving a summon (that's still running off of someone's subconscious) a specific job in advance.