You're right, these are not "normal" 26" tires, they are the 26 x 1 3/8 variety also designated as S-6, EA-1 or 597mm and are not the same as the 26 x 1 3/8 designated as EA-3 or 590mm (commonly found on Raleigh and other English 3-speeds). I've found the most readily available tire in the size that you need to be make by Kenda. They are not expensive and most bike shops can get them if they don't have a couple in stock. You do need to be very specific about the size as they are often (understandably) confused.

Regards,
Alan