Literally, your Greek words say "... he is worthy, or [or than] the victory." It seems like the tail end of a sentence that might say something like "He is worthy of winning either the XXX, or the victory" or "He is worthy of winning XXX (e.g., the praise) rather than the victory." Now, it occurs to me that the true motto of the fraternity is in the words that begin with phi, kappa, and tau, correct? Could your "subsidiary" motto be a continuation and completion of the true motto?