The engine serial number didn't necessarily match the tractor serial number on the Dubuque built tractors, but they were recorded in the serial number register. You can contact the Two Cylinder club at Twocylinder.com and have them research your tractor. It costs, but may be the only way to tell what your tractor serial number was. Then you can apply to Deere for a replacement SN plate. It won't look like the original, but would be official.
On the other hand, if the motor has been changed, the only way to get the serial number range is to get a parts catalog and start narrowing it down based on production changes.