You are welcome.
Those are indeed the type of grips we would expect to see on a .38 Super of that serial # range. They were used from post WWII until about 1967.
Interesting, the plating appears to have been applied on top of bluing. That lends credence to your speculation your father may have had it after market plated. Most factory nickel finishes are applied to bare steel rather than to blued steel.
My copy of Clawson's book does show a mild discrepancy. Although page #222 shows gun #818777 being made in 1950, the slide markings pictured, per page 89, didn't start until 1959.
Further, the slide stop pictured (which added to earlier confusion as to whether or not the pistol was pre-WWII) is of a pre-war checkered type (p52), vs. the grooved type (p 81) 4 rib slide stop type described on page 89. Also I would have expected the trigger to be grooved (p.89 again) vs checkered.
This all strongly implies a mixing of parts (for an unknown reason) at some time in the frame's past and makes the gun a shooter.