If your '77 would have had the FE7 heavy duty suspension it would have had a 11.12MM rear bar. That's about .438 inches so even a 5/8" (.625) bar would be a heavier bar than a '77 HD. Leaving the springs and front bar original I really can't see going any thicker than that. If it oversteers really bad when pushed you might want to consider going heavier but if it doesn't, then the 5/8 should be a good choice.
Interesting fact is that your front bar is the same part number as several Corvettes clear back to 1963 including some with special suspension and some big block cars. Must be an ok bar on the front already. If you change out the rubber grommets on the sway bar links to urethane you will get sharper response, especially if the rubber ones are flattened out and well past their life cycle. Same goes for the mountings but be sure to lube them with the manufacturer's recommended lube to prevent squeaking.
Tom