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(+1)

Some ideas from the top of my head:

- You could add one space next to every open space, so it'd be a 3, 5, 5, 3 board instead of a 3, 3, 3, 3.

- You could add "day-night/reversal symbols" to the current open slots (or perhaps just two of them, although you lose symmetry) and whenever you step in one, the respective countdown goes down by one. In my mind it leads to more situations where you can account for cycles changing to make set-ups, or maybe it doesn't and breaks the current balance, lol.

- You could hard code it to 3 and 6 (or something) for the first turn.

(+1)

- Ah, right, the board doesn't NEED to be a rectangle! A cross shape could be the right direction, thanks!

- That's what I had in mind too when you talked about ways to manipulate the cycles, but that seems very hard to balance! Although now that I think of it... It could look like two little spirits (think will'o'whisps), one for each type of Mischief, so it dosn't visually overload the board. They could be placed randomly on an empty space after the second or third move, and work exactly as you described: land a piece on it, you either activate the Mischief, or accelerate it by one turn, then it reapears on a another empty space.
I'm not sure if it will work, but there is definitly some idea here.

- I wanted to do something similar by decreasing the range for the first cycle (like 2~4 for D/N and 5~6 for reversal). Fixed values can also work, but you lose the random side of the mischief, so I'll have to test around with different solution to see what works best.