Right now SSS stuff doesn’t work with static lighting at all, we might be able to improve that in the future.
If you ever put an area light source inside some shadow casting geometry, there are going to be some problems. The Lightmass algorithms are setup to handle area lighting between the light and the receiver, but not inside the light source. Probably what we are going to have to do in the future to solve this is to couple the light source mesh together with the light source, that way we know what part should be ignored during the shadowing.
It would be possible to switch to static lighting for overflow lights but I don’t think it would be very useful. One of the defining properties of Stationary lights is that you can change their brightness and color at runtime, if you can’t do that then it shouldn’t be called a Stationary light IMO. Note that right now, you can make them switch to fully lightmapped yourself by changing the overflow lights to Static.