This might help:
http://sight-creations.com/fxexchange/Cutouts.zip
It's an "effect" — apply it to a clip. Combine your shape generators in a stack and create a compound clip (make sure the length of the shape generators is as long as your cut needs to be!)
Click on the Drop Zone for this effect and choose a first frame (an "early enough" frame) of your shapes compound.
The default blend mode is set to Stencil Alpha (similar to luma - but guaranteed "opaque" cutouts with shapes). Try the other blend modes - you get some interesting effects and you can "double exposure" clips with it (overlay, hard light, color burn, etc.)
Stacked shapes generator:

the compound clip:

All your collected shapes in "one throw":

The drop zone also gives you scale and pan controls to help you resize and align the parts.
If you need help installing:
https://fcpxtemplates.com/installing-plugins-for-fcpx/