How could that work? First of all, a fluid confined to a sphere can not have independent great circle orbits, so the material he is describing is extremely exotic. And its still totally possible to have a continuum of angular momenta if we imagine such a weird substance could exist.
In any case, no where in his big weird book does he delineate the precise physics of such an exotic substance. Like literally show me in his text where he calculates the energy levels of say, helium, beyond a first approximation. Regular old quantum mechanics and perturbation theory is totally up to this fairly simple task, but I don't see any such calculations anywhere in BLP's textbook.