Is it possible to combine DFAO from movable skylight and GI from stationary?

I really like soft GI from stationary sky light with ability to control it for day-night cycle, however DFAO is amazing too.
Stationary GI and DFAO does not interfere with each other, but I can’t have 2 different sky lights in the scene. Is there any way to have both?

Not possible, as the documentation also states that all static lighting needs to be removed when you want to use DFAO.