The math is helped by the fact that at an extremely local scale, as you zoom in closer, hyperbolic space behaves just like regular space, so reflections and rotations and stuff work exactly the same. I essentially use regular physics simulation for collisions that, at the instant of impact, consider things to be in euclidean space to do the maths, then just continue moving things with complex hyper-math until another collision.
However, the speed of the ball is tied to the difficulty, and I wouldn't want to involve the player's velocity else the ball's velocity would be affected, wonking up the difficulty.
...Maybe I should have had the player intangible while moving regularly too? But yeah, being intangible is quite useful for keeping things simpler for longer, which goes against the intention to have you engage with the hyperbolic space.