Spin transport in magnetic insulators is often treated by assuming that magnons carry a fixed spin angular momentum of ℏ, which does not hold in general, however. Here we calculate the magnon spin angular momentum of a layered antiferromagnet as a function of applied magnetic field and wave vector. We show that the triaxial anisotropy and intralayer dipolar interactions in bilayer CrSBr renormalize the magnon spin angular momentum, which diverges upon field-induced magnon softening. This divergence gives rise to a pronounced peak in the thermal spin Seebeck response and provides a clear spin-caloritronic signature of soft magnons.