Nigel,
Kontakt is a pretty complex tool, and I am sure the factory sounds are better than Coyote...(I have it)
You just got to tune it for specific song. That being said, it seems like you are looking more for a balanced set of sounds in a single bank...like keyboard would have.
I do not believe there are any good "balanced" libraries out there for Kontakt. Kontakt is all about individual instruments and specific oriented libraries. That is where strength lives. Kontakt is not GM compliant, everything has to be assigned manually.

The only "all in one" GM solution that has a good overall sound is Halion Sonic (full)
My second choice is Synthfont VST which is included with BIAB + a decent GM bank.