Is it possible to create a balance board that follows the mouse?

I’m trying to build a balance board that follows the mouse on the Z axis, but so far every time I try, it always messes up the tilt of the board itself.

An older question of mine reminded me it was possible to make a basic balance board:

Balance Board

However, I’d like to add mouse-following to that, but I’m not sure how without disrupting the angle, and with a rigidbody things get messed up.

Yes, it is certainly possible.