Nice project!
Perhaps TPO or that other EPDM
TPO loves full sun; it thrives under it. However, since you are considering a barrier material as a sandwich/vapor barrier hdden from the direct incoming solar, you may want to consider EPDM as that layer.
Before proceeding, contact the EPDM applications engineering people at the manufacturer, and run the idea by them first (i.e. the best adhesive, compression & shear {the EPDM will act as as a rubber shock pas of sorts}, etc...) and the temperature environment (the EPDM will be operating n a potentially extremely high heat environment)...
Cheers,
S-
