It sounds like you're creating the filters off the Synchronized Data Extensions? 

When you create the Filter Interaction, it does indeed create the resulting data extension under the same folder as the root, and as you discover you are then restricted in moving it from Synchronised Data Extensions. 

I personally find SQL as my preferred approach to segmenting / filtering when it's an automations and Journeys. SQL performance is also more optimal than a Filter. You can also structure how you want your output location and data extension structure.