I don't know about UVMapper Pro, but LithUnwrap and Ultimate Unwrap3D have such a feature. It's fairly limited with LithUnwrap, though (you can only convert two selected triangles at a time, and they must be both adjacent and coplanar).

Anthony Appleyard has a utility in Free Stuff that you might find useful.

I've had problems with those Toon shader dots, also. Do you really think triangles are the cause?