Nice rifle. I too, am sorry to hear about your father and you have my condolences.
The stock is off of a WWII 03-A3, indicated by the cut for the A3 lower handguard retainer, the lack of finger grooves and the inspectors stamps in front of the trigger guard. If I could see the cut for the lower band spring, I could tell you whether it was from a Remington or a Smith-Corona, but in reality it would make little difference.
For some reason, it is fairly common to find Mark 1's that still have their original barrels, probably because they were made after WWI and didn't see a lot of post war service. I suspect that since the stock has been changed it is likely that the unique MK1 trigger and spindle/cut off have been changed too.
I would place the value on it at $700-800 as a shooter grade '03 Springfield. I have a 100% original Mark 1, and it is a great shooter. I load ammo for it to duplicate the original service loading and am sure it is more accurate than my aging eyes will allow.
Note how the stock is cut lower around the Pederson ejection port:
The majority of Mark 1 rifles were inspected by "WJS" at Springfield Armory:
This one still has it's WWI dated sling:
