It's the width coil. I bought a miscellaneous collection of them on eBay (you pays your money, you takes your chances) and the least likely candidate of the bunch is the only one close to working correctly:
close enough that I might button it up with that coil and and call it good enough
if I cannot locate the true and correct one.
The Hallicrafters part number is 51A1261-C. Can anybody cross that to a Stancor or other standard replacement part number?