rotating and sliding

I’m trying to make a rigid body slide along a rotating axis under the influence of gravity. This is difficult because the slider rigid body constraint only uses the axis at the beginning of the simulation even if the empty rotates.

My method:
“limit location” and “limit rotation” constraints in the local x and y coordinates of the rigid body object that I want to slide
“child of” constraint for location and rotation on the rigid body object targeting an empty
2 passive rigid bodys parented to the same empty at the limits of where I want the object to slide
Animated rotation of the empty

the active rigid body behaves strangely and seems to obey gravity based on its local coords when I want it to follow global.

Here’s a gif of where I am at
I would appreciate any ideas and help. Let me know if you need any more info. Thank you.