I second Ian's opinion about doing parts like this while still on the end of the bar, with the last op being to part it off,complete.
However there are a couple of things you can do now.
If the 7BA thread is tapped already, you could make a 3/16 dia mandrel with a stub of 7 BA thread on it, Thread that into the part and hold the whole thing in a 4 jaw chuck or a vise, gripping both the mandrel and a bit of the unslotted square, while you cut the slot and file it or mill it.
Or you could make a brass rod end with a hole a thou or two larger than the 11/64 stub and soft solder the part into it temporarily to make a bigger handle to grip the part in a vise for cutting or milling the slot. The slot can then machined. and the solder melted to separate the finished part from the rod, and excess solder wiped away.
Good luck, JD