I have only tried Rhino, but generally I use freeware. The same problem in there except not even possible to try convert a mesh to surface. But my shapes are extremely simple and I found 2 workarounds
- draw manually a spline through the available cutting points or
- convert also the surface to a mesh, split with it and draw a spline along the edge
The spline can be projected onto the original surface and used for trimming
Unfortunately these are practical only for simple shapes.
The following should be possible, but I have not used it:
Import a heavily decimated (=simplified) version of the mesh and try with it. Alternatively slice your mesh smaller with planes or other simple meshes in a proper mesh based program, leave only the needed part for the intersection.