Or can I just ground the device to the box and leave the grounds as they were originally installed in the 1960's?
You can but the Code did not permit the installation in that manner when it was installed (at least I don't think it did).
Also at the main panel I'll have to unwrap the ground from under the metal romex clamp and connect it directly to the ground bar, as well as unwrapping the ground wire at each outlet box from under the box clamp and splicing them together and pigtail to the box and also to the device itself. Right?
Again IMHO, you are correct.
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Charlie Eldridge, Indianapolis,
Utility Power Guy