I found the answer to this almost immediately after I posted the question. This can be added by adding the application settings in the "Settings" section of the website on the Cote d'Azur.
The following parameter will force Kudu to properly convert web.config:
SCM_BUILD_ARGS -p:PublishProfile=CloudTEST
Where CloudTEST is your web.config conversion name.
This solution is documented here.
Votive
source share