Agreed. You have just one working surface in your drawing, and it's huge, with nearly 180,000 points. That makes working in the drawing slow and awkward.
Make a new surface (or use the empty Surface1 that already exists) and add your breaklines to that surface to make the pit. Next make a new empty surface, which will become your final combined surface. Paste in the Hamilton surface, then paste in the proposed pit surface.
As for the points, change your Surface Style to include points in both Plan and Model views (there are separate tabs for each in the style editor). With points visible, use the Toolspace, Prospector tab, and expand the tree for Surface -> Definition -> Edits, and select Delete Point. Then click on and delete those points at the tips of the peaks.
Here are before/after screenshots showing one point before and after its deletion. I used 3DORBIT to get a perspective view so the peaks & their points are easier to see (this is where the Model component of the surface style composer is important. A style can have different settings for Plan view (top down) and Model view (which can be from an isometric perspective). So I took the extra step of changing the Model view surface style to include the points, triangles, and border, so that I could find the points at the tips of the peaks in this perspective view).


Jeffrey Rivers
Win 10 Pro 64-bit, Intel i9 3.7GHz, 64 GB
NVIDIA RTX A4000
C3D 2020 V13.2.89.0