Confusingly, you can statically link a dynamic library (i.e. the dynamic library includes all its dependencies statically instead of recursively depending on more dynamic libraries). You can even link it in such a way that the dynamic library gets its own version of each dependency regardless of what the main executable is linked to (otherwise the main executable's links could override yours).

I did this once with a ruby gem that had particular c++ dependencies that kept breaking when the build machine had different library versions than the production machines. If you aren't integrated directly with the development of a linux distro, it's best not to use their packages as runtime dependencies, since they really only consider their own use before changing things up.