"off the top of my head I was just gonna modify the ball's velocity randomly and check if the player tilted too much in a certain time threshold"

If it's any help that's pretty much how I've done it. I've not gone for a "directional" tilt, you just basically shove the bottom of the table forcing the ball up.
In saying that, I've not quite nailed it yet, at times it can look a bit like blow football.

Squize.