My current Z4 had the same issue with the passenger side one not seating, but it also leaked enough to empty the washer reservoir in less than a day!
I got really lucky and found a used pair on here and Ross at RBM swapped it but had to remove the wheel-arch liner to get to it, but that's probably easier than risking those bumper clips!
After it was fixed I took out Fuse 40 so no more headlight washers, but no more streaks up the wings or missing headlight washer caps/jets.
Hopefully Rucky's suggestion will work, but be careful as the "D" clip on the top of the jet that secures the cap can be fragile and I don't think it can be bought separately.