The static build is failing inside of Yocto. All I have done to get this to fail is to change -shared to -static inside of qtbase.bb and then $ bitbake meta-toolchain-qt5. Building Qt dynamically will successfully create the SDK, but not statically.
I have found someone with the exact same problem here. The plugin lib directory path is incorrect and has the cross compile prefix omitted causing problems finding the necessary libraries.
I've posted my build environment and error output here.