Aftermarket wheels in 15" diameter are generally going to be available in either 8" or 8.5" width, and from there they jump to 10" wide. For a 325 section width, you'd definitely need to go with a 10" width.
While wheels were specified by offset for years, the more common figure now for aftermarket wheels is backspacing. Offset is a measurement from the centerline of the rim to the mounting face. Backspacing is the measurement from the back side of the wheel to the mounting face. Your pic from the rear shows that you can't stand to have a wheel with more backspace than you have now, else the tire would be into the spring.
My guess is that your current wheels are 7" wide as that's the most common width for 15" Cragars. So, if you went to a 10" wheel, all the additional width would be on the front side (outside) of the wheel. At that point, there's no question that your 325 tire would be hanging outside the wheel opening. Glad to hear you don't want that, as it's one of those things that just screams that the car belongs to some goon who thinks a cartoon car looks good.
Don't be tempted to put a 325 tire on an 8" wide wheel. As mentioned above, it will compromise the tread life somewhat, but the stiffness of the structure under the tread makes this less of a problem with radials than it was with bias ply tires. The real problem with mounting tires on too narrow rims is that it decreases the lateral (side to side) stiffness of the tire. IOW, it makes the wheel want to wallow around with respect to the tread in turns, and has a major detrimental effect on handling.
If you were to go with an 8" wheel with 1/2" less backspace or an 8.5" wheel with the same backspace as now, and maintain the same 275 tire width you have now, it would fill the wheel well much more than the current setup without getting into the problems of hanging the tires outside the body. Either combination would move the outside face of the wheel 1.5" further out. In practical terms, a 275 section width is about the widest tire you can keep within the fender on any 60's era car without major body modifications.