I agree. Use modern wheels from a 'disk brake' Ford. They are usually 14" X 6" with vents. The vents mean nothing, especially if you use a full-wheel cover.
Cars from 1960 did NOT have disk brakes so clearance was never an issue. Instead of welding the wheels together, back then, Ford used rivets with inner tubes. Tubeless tires first came out in the 1957 Chevrolet, and Americans did not trust them.
Here is an example of the 14" wheel you want:
Measure from the flange that rests on the drum/rotor (in the rear of the wheel), to the outer edge of the wheel. This one has a back spacing of 3-1/2", which is perfect. Also notice the 'hump' on one side of the rim, for caliper clearance. <--this is important. Here is the caliper clearance picture:
It's just enough.
Modern wheels are spot welded together. eliminating the need for rivets that protrude. Good luck and I hope you don't spend good money after bad. Otherwise, you will soon be in the market for proper wheels. - Dave