New pickups?
Anchoring on the pickups is fairly standard technique for many players- as I have witnessed here and on many other forums and instructional videos.
Perhaps a thumb rest/tug bar-type contraption? (Tug would be on G-string side) $3.49 plus shipping on Ebay.
My first no-name Fender Clone had one of these, way back in 1984. It was probably a decade old when I took possession. I didn't understand ANYTHING about bass technique at the time (not drastically different than the present

) However I seem to recall that I sort-of figured how it worked. ( Photos from random ebay listing)
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