I wouldn't leave out the Shadow NFX if you haven't decided yet. You get two foils with a 1/10" plug, intended to be used on both bridge feet, but you only need one of the foils. Put one of the foils under the E bridge foot of both basses and only swap the battery adapter. One plug and one wheel that could easily changed in seconds.
I'm sure the sound will be much better with bowing using the Shadow NFX than with the Bassmax. And you don't need an impedance buffer.
On the other side, if the basses are mostly plucked, then the Bassmax might perform a bit better and if the instrument is moved (but not the other) you don't have to care about which bass has the battery adapter mounted.
This is an interesting looking pickup. Playing around with the idea of putting a pickup on a cello (mine, not a school instrument). If there's a cello version of this, might be worth considering. Cello would be bowed and plucked, whereas student basses in the jazz band are mostly plucked. I do worry about anything under the bridge foot marking the top or impacting acoustic sound, though... don't think I'd put this on my primary instrument. The Band looks interesting, too. The cello pickup is not an immediate concern, though.