I suppose an easy test as to whether the hum is induced by the amp would be to relocate the table temporarily.
If that helps, have your local hardware cut you a piece of metal to set the table on as a shield?
I'd still lean towards the cables being the problem, especially on an older table. Those have potentially been yanked and twiddled a LOT in 40 years even with the best of care. First step for me would be to clean the connections, inside and out, with D5 and tighten the prongs.
The Signet connector cleaners are right nice, and if nothing else, will eliminate the RCA's as a problem ...
Could also be cold solder or dirty connections under the table as well. Maybe have your tech look at that if you're not comfortable digging around inside. Or, as I've seen with several tables, broken wires right where the cables exit the table body.
Another common problem is improper grounding. Yes, you should run a ground from the table to your amp/receiver, but don't forget to ground that as well.