For features like overlapping polygons that would require ACE (as EasyGerb just simply converts selected objects to Gerber). ACE is a stand-alone tool that can easily convert DXF/DWG files to Gerber, plus it has a similar interface to EasyGerb (i.e. select layer options, etc.) for easy learning.
Here's an article I wrote about AutoCAD to Gerber conversions that you may find helpful.
Here's a forum post which may help: