As the OP has demonstrated, "Contact the library's authors and negotiate usage of the code under another license" is EXTREMELY difficult for a project maintainer and would thus be near impossible for anyone else.
It is much better if the price and terms are simply public up front. For instance, we were worrying about PyQt (GPL + commercial option) vs. PySide (LGPL) for a project, where PySide didn't support certain things that we needed. But then we realized that the PyQt commercial license comes with reasonable terms, and costs only £350, and it wasn't even worth the time worrying over it any more.
So yeah, "contact the authors" can be hard, but an up-front agreement and price can make it pretty easy.
So yeah, "contact the authors" can be hard, but an up-front agreement and price can make it pretty easy.