I purchased this clock about 12 years ago and would like to replace the string weight cables with something more like the original. It looks like the cable drums would take a 1/16" steel or brass cable with a compression stop on the end. Or would a gut be more appropriate?

the weights are 7lb ea.

Not sure the years that was manufactured, but some of those had good cords, not cable. I would recommend to do more research before I'd install wire cable. Personally I think the cable would be stronger though. Hope you get it like you want it, that's a nice clock for sure.