Most axles are going to be too wide. You need a Mustang 9" to bolt right in, and they are expensive if you find one. Even the Explorer axle is about 3" too wide. Your best budget bet is a 93+ Ford Ranger 8.8". It's 1.5" narrower than the Explorer (only 1.5" wider than the original Rambler axle) and has drum brakes. A Ford 9" or Chrysler 8.75" would be more period correct, but also cost more and need to be narrowed. I'm not sure if you can find a Mustang 9" cheaper than narrowing a big car 9" or not, you'd have to look into that and see. Are you going to tub the car for wide rear tires too? Then the axle will need to be even narrower (or just order the right offset wheels). If you're tubbing it you could use an AMC 20 axle (8-7/8" ring gear) from a CJ-7. It's about 3" narrower than the Rambler axle. It's tough enough, and I think the CJ axle used a one piece axle/hub instead of the bolt-on hub that the cars used. The drawback is it uses a 5x5" (or is it 5x5.5?) wheel bolt pattern -- you'd need to redrill the hubs for a more common pattern.
Do any of the 9" ford or 8.75" Chryslers have an offset hog head? If so get another short side axle and it's easy to shorten just the tube on the long side. That might not narrow it enough though, the American is pretty narrow.