removing broken off screws - tip
Because this comes up, more often than anyone would wish... So the screw head broke off flush. It's a cast iron machine (not so easy for an aluminum 201 or 301, you would need to find someone with an EDM machine at a machine shop).
At my local hardware/lumber yard, which is an Ace franchise I believe, they have left handed drill bits, which are one way of removing broken screws. The trick is, to get a centered start on the hole. Using a Dremel style grinder with a pointed (Harbor Freight sells diamond tip mini grinding points) stove, level of the top of the screw enough to start a center hole. Put a little divot in for your drill bit to start with, then, using a drill press, most likely (unless you are super steady and a sure shot) drill down with the left hand drill bit. This may actually break the screw remnant free and start pulling it up. Now the smallest left hand bit they had, was probably good for a #6 screw, not sure. But I'll bet McMaster-Carr or someone else sells ones that are smaller.
I noticed they carried one uncommon thread tap, I believe it was #6-40 which is the size of Singer needle plate screws. If they had a die, one could make some screws, if rather codgy looking ones.