São José do Rio Preto
I like to resolve these as fractional Priorities:
+.4 -- Wins Priority ties without clashing
+.3 -- Jager Signature Move
+.2 -- Finisher
+.1 -- Fighter on the team with fewer fighteres
-.4 -- Loses Priority ties without clashing
This clarifies the order of precedence and also rounds correctly for effects that care about it, e.g. Lymn's Disparity and Ottavia's Target Lock.
There is at least one mistake in your list, in that Jager's signature moves LOSE to finishers, but win against everything else.