The 88407 number I believe came from the yoke cut and is the "assembly number", not the serial number. As others asked remove the target stocks and give us the serial number from the butt of the grip frame. It will be a single letter and up to 6 numerals. Since the gun has S&W target sights the letter should be "K", which is part of the SN.
Other than this the gun is no later than the late 1940s (Single line address on frame) and is a custom target pistol for, probably, bullseye shooting. It has a custom barrel that appears to be 8 5/8" from your photo. A full-length barrel weight has been screwed to the bottom of the barrel, one screw is visible in the photos. The S&W hammer has been modified by either welding or re-forging to create a wide hammer spur. Since it is so thin it was probably re-forged, a fairly common modification in the days before the factory .500" wide target hammers were available.
I have no imaginable reason the barrel would be partially smooth bore unless it is at the breach end! If the breach is free-bored it could be what is referred to as "Taylor Throating", which was popular at one time for target pistol barrels using cast bullets. 1 & 1/2" is a little excessive for Taylor Throating though. It would usually be no longer that the bullet the owner would be loading in his ammunition. Let us know which end the free-bore is on and it might make sense.
I cannot see anything about the gun that would cause me to believe it was anything except a post WWII K-38 that has been extensively modified, certainly not a "Victory Model".
