Makes me wonder. A .44HE 2nd would not have a large underlug, just a little piece in front of the ejector rod. They can also have 5 digit assembly numbers. The serial number is the one on the bottom of the grip frame. The number in the crane cut on the frame is an assembly number. Just checking to see if #11013 is not the assembly number. If your gun is a .44HE 2nd it also will not have the "triple lock" which is the little piece you see in the frame near the bottom of the ejector rod shroud in the pics here.

A factory refinish could be marked with a star on the frame where the serial number is. There could also be a month year, like 3.50 on the lower right side of the grip frame under the grips. These markings do not mean for sure refinished but probably.

Having just lost my father a few months ago I can understand how you must feel. He has left you a wonderful gun no matter which model it turns out to be.

Welcome to the forum.

Bob