A friend of mine has 2 63 Falcons, one a stockish 302/auto, the other a built 302/t5z. Both started with the original 8" rears. The stick car (convertible) has broken the diff a few times with various causes. What I can say from his efforts is that in about 72 Ford changed the center section to a beefier design, along with straight axles versus the older ones that neck down after the splines. He was able to cut later model axles and respline them himself, use the later model center section, and get an aftermarket 4 pin carrier. So far he has yet to break it using a 235 drag radial and 1.6x 60' time. The friend Im referring to is pretty handy with a lathe and has his own bridgeport, you may not be so lucky. Either way its not much to have an axle cut and resplined.
Im a little surprised nobody has mentioned using an Explorer 8.8 diff. They can be had for $150 all day long around here and have 31 spline axles, disk brakes, correct bolt pattern, and most have 3.73 gears with posi. You will have to shorten one side and buy another short side axle, then have the perches moved, but its still a pretty strong cheap rear end. Only drawback is that by narrowing the one side it doesnt come out to EXACTLY the width of the original rear end. This is no big deal if youre getting custom wheels or using late model take-offs with spacers, but it may present a problem when re-using original wheels.