Wow. Now I know what my Steptoe No. 0 was modeled after. It's of the same approximate vintage and is very, very similar in appearance and size (I wish mine had a vertical head on the overarm as well). The functional condition of mine was pretty good when I got it, but it looked horrible. I've started half heartedly pulling parts for restoration, but won't get into full swing until my 13" South Bend Lathe is finished. Do you happen to know what the taper is in your spindle? As similar as the machines are, I wouldn't be surprised if they're the same. Mine has no door on the side and my overarm clamps are on the right instead of the left. Other than that and mine having back gears, they're nearly identical.
My spindle taper appears to be similar to a Morse taper. I Tried a MT3 center from one of the lathes and the spindle swallowed it. I don't have a MT4 to check, but I believe (based on dimensions) that a MT4 is too big. I'm starting to think it may be a Brown and Sharp taper (or something similar).