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We extend the recently proposed SU(5)×T13 model for the asymmetric texture to the up-type quark and seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vectorlike messengers. The complex-tribimaximal seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with mν1=27.6  meV, mν2=28.9  meV and mν3=57.8  meV. Their sum almost saturates Planck's cosmological upper bound (120 meV). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the CP Jarlskog-Greenberg invariant to be |J|=0.028, consistent with the current Particle Data Group (PDG) estimate, and Majorana invariants |I1|=0.106 and |I2|=0.011. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter |mββ|: 13.02 or 25.21 meV, both within an order of magnitude of the most rigorous experimental upper limit (61-165 meV). [ABSTRACT FROM AUTHOR]