I have pushed changes in the maximal branch for this. It is now massive quicker to calculate the 'maximal subgroup type' maximal subsemigroups of an inverse Rees 0-matrix semigroup (i.e. one with only one non-zero entry in every row and column).
However, the general code for inverse semigroups is still slow (although much improved). Since the principal factor of a D-class of an inverse semigroup has (in general) a huge number of maximal subsemigroups of maximal subgroup type, we are still left which the hard task of calculating (brute force) which of those maximal subsemigroups of the principal factor correspond to a maximal subsemigroup of the whole semigroup.
I am unsure whether it is possible to improve this aspect of the code.