BRep ConvertToMesh with Faces property matching the original BRep Faces property

I need to convert a BRep entity to a mesh where:

1) the mesh edges and vertices are shared on the common edges of the faces

2) the triangles are grouped based on their BRep source face.

Goal 1) is met using the ConvertToMesh method, but the face-triangle association is lost.

Goal 2) is met by joining the faces via tessellation, but sharing the face vertices is not.

Is there a way to satisfy both of my requests?