Thanks everybody!!

I decided to try the thin double sided tape idea first. (BTW the part is
not round so some of the replies would not work). Milled a thin slot across
a 1" x 0.1" piece of aluminum. Slot depth approximately 0.025" deep.
Simply enough to give me a shoulder against which the part will abut while I
push the file. Used thin scotch brand double sided tape. Worked like a
charm. Merely sliding the file across 4-5 times, I removed almost 0.010
material. Was shooting for 0.007±. Very fast. Takes longer to find the
end of the scotch tape than to complete the project.
It surprised me that I could even file backwards, whereby only the tape was
holding the part i.e. no shoulder for the part to rest against.

Thanks!!!!!!!!

Ivan Vegvary