  We formulate a version of the low-scale Majoron model equipped with an
inverse seesaw mechanism featuring lepton-number preserving dimension-6
operators in the scalar potential. Contrary to its dimension-4 counterpart, we
find that the model can simultaneously provide light and ultralight Majorons,
neutrino masses and their mixing, while featuring strong first-order
cosmological phase transitions associated to the spontaneous breaking of the
lepton number and the electroweak symmetries in the early Universe. We show by
a detailed numerical analysis that under certain conditions on the parameter
space accounted for in collider physics, the model can be probed via the
primordial gravitational wave spectrum potentially observable at LISA and other
planned facilities.
