You shouldn't care that much about ngones or tris, just add a subdivision level to your mesh before import/conversion.
By doing that, you will always end up with a full quad mesh.

What's important, is to 'hide' as much as you can any vertex that is not connected with 4 edges.
The surface quality in those 'poles' area will always be a problem (surface continuity problem, or pinch).
By hiding, I mean avoid to place those vertex where there is a big curvature change.

I have to say that MAX SubDiv script is doing an amazing job in that area, way better than anything I have seen so far.
It's very obvious in your example, the middle area where 12 edges are connected to one vertex looks much better (I would even say perfect) with Max's script than Rhino result.

The only thing missing in this script, is a surface simplification pass, to reduces the total number of patches.
I still can't believe this is "just' a script Oo