I'm going to assume that the radio is the factory original since you stated that you tap it by the Delco marking or has the original been swapped out?
Sounds to me like the tuner inside the radio is going out or possibly a bad solder joint somewhere inside the radio....unless you are an electrical whiz I would just replace it.
I would think that a bad ground would kill the radio outright and that would be easy to find?
Ever thought about changing to an aftermarket radio?....they start out fairly cheap on Amazon... $20-300.
If you want a factory original..... I've got 5-6 setting on my shelf that will eventually get tossed.....
[This message has been edited by MadProfessor8138 (edited 09-06-2017).]