I ended up writing some code to build the library using system() calls. The toolbox is essentially a single class and when it gets instantiated, the ctor checks whether the binary library file exists and otherwise calls the function to build it from source.
Don't know if that's the best way, but it seems to be working. Thanks to CMake, it's also fairly easy to do platform-independently. But it does require the user to install some software beyond Matlab, namely CMake and some compiler.