Most events I don't move mods around for because it's a hassle. I also upgrade to six stars where it is needed.
The concern that not modding a character with the best mods will make a difference is just overblown. So far we have seen two types of events. Those that have a rush to 7 stars but require low gear and those that have plenty of time to farm but require g11 or g12.
For the first, if you get the stars, you can beat with mediocre mods. If not put a bit of exta gear on and you can.
For the second you're going to have to have part of your team g12 anyway. For chewie I had boba g12 and for 3PO I have elder g12. So no, I can't use all my 6 dot mods but I could use some if needed. For chewie I didn't for 3PO i put arena speed mods on elder and decent mods on the rest. I beat both events 7 star.
So it's not worth doing worse in tw, tb, raids, and ga to maybe use that mod for some event.