I had the same problem with my 4004 earlier this year and fixed it mid-June. See attached photos for reference, specifically the 1st one (I am showing a DIN7 plug, but only pins 2, 3, 5 and shield are required for functionality), while the 2nd one really shows that the system ground and signal ground must be one and the same! This is specific to the Beogram 4004 version only!
Back to your DIN plug coming out of the 4004, need to open it, make sure that the black wire is disconnected (desolder it and tuck away) from the plug housing, than take the shield wire, connected to pin 2, split it in half, and solder part of it to the shield of the plug (in place of the black wire)! This way, system GND and signal GND (L/R low) of BG4004 will be at the same potential, so should become independent on the RIAA types/models and how they have GND implemented internally…
Courtesy of Rudy, aka Beolover, he confirmed this for me as well:
“It is my experience that connecting shield and system ground usually takes care of humming. In later 4004s they actually implemented this as factory standard on the output board. It only took them ~5 years to figure it out back then…”