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I bought one of these for my vintera jazzmaster to put under the pick guard when I swapped the tort guard for a white one and it helped a lot with the noise. It wasn’t anywhere close to what you are hearing with yours but it might help?
The changes have only been cosmetic because I didnt like the tort guard.
I got an aluminum pickguard shield from amazon for $30
Chrome tele knobs for $14.39
and a white pickguard for $11.75 and put Ernie ball slinky 11-56 strings on it and shimmed the neck with a stew mac .50 degree shim and it plays great.