We calculate the temperature T and angular (θ, φ) dependence of the upper critical induction Bc2(θ, φ, T ) for parallel-spin superconductors with an axially symmetric p-wave pairing interaction pinned to the lattice and a dominant ellipsoidal Fermi surface (FS). For all FS anisotropies, the chiral Scharnberg-Klemm state Bc2(θ, φ, T ) exceeds that of the chiral Anderson-Brinkman-Morel state, and exhibits a kink at θ = θ * (T, φ), indicative of a first-order transition from its chiral, nodal-direction behavior to its non-chiral, antinodal-direction behavior. Applicability to Sr2RuO4, UCoGe, and topological superconductors such as CuxBi2Se3 is discussed.