I have had bad luck with my stock rear axles/differential. Once a tooth flew off the ring gear while on the freeway, punched a hole in the casting, on other occasions, twice I have broke axles, and twice had them slip out on me. So when I had my differential rebuilt by J&S Gear in Huntington Beach CA, I had beefed up axles installed. He got them custom machined from somebody in Oregon as I recall.
If you are not worried about being dinged at a judged car show for originality, you can install a bullet proof Dana 60 axle under you car out of a Ford pick-up truck that has been shortened and has custom axles with the required brackets for mounting it in your car already installed as sold by Currie. Or you can install a 12 bolt from a 1965-'70 Impala by changing the mounting brackets over to match your car.
Your rear end was designed for a 150 horse power stove bolt 235 cubic inch six cylinder. The 265 cubic inch (that later swelled to 283 cubic inches) was an after tough. Because the same axle was used and broken every weekend behind a 348-409 motor Chevy was forced to buy a stronger axle from Spicer Dana corp in 1965 to reduce warranty claims. Usually the spider gears break first, then the axles let go when thicker spider gears out of a MOPAR rear end are installed. Custom alloy aftermarket axles (from Moser, or Strange Engineering) will give you a 20% increase in strength.