I hope I understood your goal correctly: you want to be able to implement a custom set of equations inside the "Spatial Contact Force" block. It's not directly possible, but here is a workaround I can think of:
(1) still use the spatial contact force block, but make it very "weak", meaning low contact stiffness, damping, etc.
(2) use the sensing function of the block to get information like penetration depth, direction, etc, for your own calculation of the contact force.
(3) Apply the force with an external force block. Make sure apply opposite forces to both bodies in contact.
(4) you may also sense the contact force itself, which should be very low, and counter that with an external force block.
I also suggest that you try to write your own contact force equations in Simscape language as a .ssc block, probably using the physical signal domain. This way it won't need to going to Simulink and back to Simscape, saving some overhead.
Just a thougtht. I haven't done this myself before. Hope this helps.