OK, so it's only one full tank, but it looks like the v1 pin in the v2 Diver in the BB is the answer. I just finished off a full tank of juice with this setup, and not a drop, not a gurgle.
Well, there was one difference.
I just received a massive order of juices from Ahlusion, including (by accident) two bottles of Maple Dream. I wasn't too impressed with it, as it seemed to have almost no flavor (like I needed another Ahlusion juice addiction). Now, with the v1 pin, and I know this sounds crazy, I'm actually getting quite a bit more flavor out of this juice.
Note: I filled using the fill port.
I'll keep running this setup over the next few days, to see if anything changes.