Hey Ghostyhead!
Never had an issue on my old MK standard. That had the default space of around an inch and a bit between the end of the fretboard and the neck pickup. Always seemed plenty of space to get the forefinger under the strings for popping. No issues now with my SC deluxe, and I think it has basically that same default space. But I have seen some MKs and SCs with the neck pickup rather closer to the end of the fretboard - I guess the original owners must have specced them this way, perhaps to get a slightly bassier sound, or maybe Alembic used a different default during a certain period of production.
Anyway, if you can post a pic of the bass you're talking about, I can at least tell you if the space is the same as on mine (in which case you should have no problems), or a smaller space (in which case, t might be a bit tight).
And I'm pretty sure you can't lower the pickups until they're flush with the face of the bass - the pickups are installed in such a way that they sit on top of two of the four securing screws, and I suspect those two screws are too long to let the pickups go down that far. Could be wrong, though - I've never tried it - but the reason I've never tried it is that the response drops off very quickly as you move the pickups away from the strings and it becomes less than ideal after a certain point.
K.