Take the skin off as much as possible with a carbide burr or small grinding bit in a Dremel or die grinder then file out the corners and tidy the faces with a file.
You say the part cannot be machined but why can't you mill out to the 7/8 square and then just file the corners if you don't want an internal radius. You could also knock up a tool like a slotting head and plane the corners out. I think filing alone will not give a good sliding face unless you are very good at filing or use a rest.
To help people see what you want to do, this is the part in question

J
Edited By JasonB on 25/03/2012 08:16:43