On one occasion the I let it run 24 hours and it did not complete the extrude, but the MacOS did not complain about fusion not responding. On other occasions Fusion did not actually crash but the OS indicating that it was not responding for several hours.
I have found a work around where I extruded by a fixed distance past the object surface and then used the combine tool to find the intersection of the two bodies and delete the overlap. This compute completed in a few minutes, so it does not seem that the computation time of the extrude to object should have been the problem.
Here is a link to the design.
https://a360.co/3J2r1P7. Body 26 was the problem.
My immediate issue is resolved, so I am happy to close the case unless you want to follow up some more.