BigH,
one easy way of doing it sure would be thru geomechanical classification of rock mass (RMR, GSI),which yields mohr-coulomb parameters to be used in one of the variations of Prandtl's equation. That is, you treat the isotropic rock mass as a soil (or as a metal as you imply).
Another way would be the lower bound mehtods you cite, T-P is probably one of them.
This paper by Meryfield, Lyamin Sloan is very good in that it uses rigorous FEM to assess the Mohr Coulomb parameters obtained by Hioek-Brown. They turn out to be under conservative.
Probably the best paper on fractured isotropic rock mass, You'll like it, many plots, it's freely available for individual use:
If the rock mass is anisotropic, then things are going to be more complex.
In the case of the fractured basalt, it would be enough though to provide the resistance of the few governing joint sets and show the available strength exceeds by far the mobilized strength.
All this for a mat with a limited loading?
Sure it sounds crazy, but if the rock is isotropic it would only take about 15 minutes to completely prove the point quantitatively. I would only need a clear picture of the rock mass.
It takes longer if the rock is not isotropic.