So you can grab and separate that piece out. select all the edges and do a join to get curves (Left in your file)
Select all the edges and hit delete to recover a sphere... rotate the speres seam edge away fro your work, then trim with the curves you grabbed.

Hi flippyfloop attached here is another version with the seam rotated like Burr's.

My method is Edit > Separate on the sphere face. Do an "untrim" by selecting one edge of it, then Ctrl+A for select all then Delete. Then Transform > Rotate > Rotate axis to rotate the sphere, then Edit > Trim and use the "Select naked edges" shortcut key (http://moi3d.com/forum/index.php?webtag=MOI&msg=6051.2) in the step where you are selecting cutting objects. Then Edit > Join to glue it back together.

- Michael

That works great thanks.
Was not aware of the Untrim function & the Naked Edges. Both very helpful.
Cheers.

Thanks Michael,
I reread my post, which was utterly unclear and insufficient..........