> Should the import logic in mpmath also use import_module?

No, just leave it as it is in the mpmath repo.

> Should mpmath also respect the GROUND_TYPE setting? If not, mpmath could be
using gmpy2, sympy could be using gmpy, and it will be difficult to
distinguish between the types when debugging.

As far as I know, the gmpy types in mpmath do not leak out of mpmath.  But I guess it's possible. 

Maybe the best solution here is to not worry about if both gmpys are installed.  If we really need to test gmpy 1, we can use virtualenv.