You know, just for grins, you could unwind the E-string, turn the ball end over and tune back up and just see what happens. Strings are a black art, and bass strings, with windings atop windings, can run you crazy chasing what you thought was an action-induced squeak. That's why I've learned to live with needing a touch-up or tweak until it's new string time: Once in a great while, just changing strings fixed it.
Also, like I said above, once you get a bass action down around .011, it's like riding around in a car that's been lowered: Even a little bump feels like a pothole. In other words, it doesn't take much at all to induce something you may now want to hear, stuff can be off / out just a few thousandths, and you know it.
That's why I always recommend tweaking action in playing position: The weight of the axe on the neck in a laydown holder could bend it enough to alter your measurements, as we're only talking thousandths here. Somebody like James at Alembic who sets them up laying down every day is a different case than the rest of us.
But since you have no 'fretted' complaints and it's buzzing open on the E (great, it's easier to chase the outside strings), that's the smoking gun that it's a hair too low either at the nut, over the last fret, or a little of both.
Every bass will 'max out' slightly differently one to the next. But generally if you're low enough to hear some string noise, etc., unplugged, but it's not coming thru the pickups, you've just about got all you're going to get.
I'm framing the fabulous quote from the previous post . . . . . Thanks, MWT ! !
Joey