Roudtrip Log-C to Linear in AE and back to Log-C for grade

Hi there,

I'm about to start work on an edit where we have a fair bit of green screen and set extensions to build, which will all be done in After Effects. It's being shot Pro-Res 422 HQ in Log-C and edited in FCP.

I understand how to convert the footage into linear for compositing work in AE, but I can't see how to output the file back into Log-C so it matches the non-fx footage and makes things work for the colorist (who'll be using Da Vinci).