Does the GPL force exclusivity for derivative works?
Yes, but the key is the definition of derivative.
The license of library (B) only comes into play if you distribute library (B) with software (A). If you release your software (A) independently of library (B) you can do whatever you want with it (though I guess making the library optional would limit the fnctionality of the software when not compiled with the library).
As such, you could release software (A) under GPL, bundled with library (B).
You could also, since you are copyright holder over software (A), release it under whatever other licenses you prefer. But in those cases your customers would have to download library (B) and compile it into your software themselves.
A better solution overall though, would be to ask the copyright owners of library (B) to offer it with a dual licenses themselves. Offering Lesser GPL could encourage commercial support for developing the library and the option of a commercial license could bring in money to support the community in lieu of contributing code back to the project.