I have a 72 4001, and I don't seem to have that issue. When I read your post, I pulled it out and played it with attention to the output of the E string, it seem to be at the same level as the rest of the bass.
Now, for the purpose of full disclosure I had a full set up done, action, intonation, and even had the pup height adjusted only 2 weeks ago, and replaced the strings. That might have something to do with it, too.
Carvin Club #303.
Rickenbacker Club #512
"SX Club Member in Good Standing"
Short Scale Bass Club #433