Which name prevails in a pair is not fixed solely by formal logic. Established usage, familiarity, ease of expression and the communicative context may shape the choice; the same explanation need not govern every example.
Al-abawan privileges ab; al-ʿumaran uses ʿUmar; al-qamaran uses qamar. Each must be recognized as a conventional expression in Arabic, not extrapolated from an arbitrary formula.
Therefore one should not invent a new dual for any two associated names merely by analogy. Attested linguistic usage is essential.