Sampling exposure (or HLS) from one layer and applying to another...

I am working on a stop-motion animation which was shot outside. So there is a lot of flickering in lighting, which is okay. But I need to erase a rig that holds up a puppet. The back template is at one lighting and does not match the front layer throughout.

I was wondering is there an effect or expression that samples the exposure or HLS from the front layer and can apply it to the back layer, so the flickering affect is translated to the back template? So let say we start with a uniform exposure in which the front and back match. Then as the front changes, we add or subtract the difference to the HLS or exposure of the back template.