I was able to split your mesh in about 70 sec on my machine with a Python script I wrote that often works with Rhino’s Mesh Tools -> Split Mesh does not. A link to a .3dm file on Google Drive with the split mesh is here:
Here is a picture of the split mesh with the smaller piece selected:
My script uses a closed curve to split a mesh. For the closed curve I used your curve which is now on layer = 3D Model:Corners:Ordinary. The split mesh pieces are on layer = 3D Model:Split:Pieces. Your starting mesh is on layer 3D Model:Start Mesh. Your other meshes are on layer = Other Meshes.
The Python script is attached. To run the script, select Split on the first line of radio buttons and select Reuse on the second line of radio buttons. Then click on Show Options button and make sure Normals is checked so that you have a good mesh after the split is complete. Then click on the Split Mesh button at the bottom left and wait a minute or so. Here is a picture showing the form of the script just before pushing the Split Mesh button:
Let me know if you have any questions or encounter difficulties running the script.
TrimMeshToCurve.py (293.2 KB)