How to I get rid of these flippin' edges? I'm trying to fill a complex face created with via an SVG, my workflow is as follows :

Import SVG
convert to mesh
simplify mesh
fill
----------this is where I'm stuck

By filling the face it's creating additional edges by splitting the faces, not the end of the world but i want to inset the (one) face so that I can bevel the edge slightly. Having these extra faces in there causes them to overlap, and creates a mess.

I've tried dissolving the problem edges, but this doesn't do anything
I've tried deleting the vertices attached to the edges, but this removes the face too, and filling the hole created just puts me back to square one.

Stumped! Please help and thanks in advance]1
You cant dissolve those edges. Some polygons simply have too many sides. I fought this many times importing project from Autocad and applying wireframe modifier for cool looking render. Anyway in case of the ring how do you imagine polygon data saved without edge going through the ring? It is simply not doeable to make one face polygon ring without edge going this way.