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Considering all possible permutations of 16 is clearly going to take a long time. So in this program I choose the two ascending sequences of 4 players that are the opponents of the finalists, and then permute the remaining 8 players. The runtime is further improved by checking the opponent sums of the 8 players we already know and if the maximum is already greater than 4 times the minimum we reject the candidate solution and don’t bother permuting the final 8 players.

This Python program runs in 6.3s.

Solution:The final was played between player 13 and 14.The maximum opponent sum is 36, the minimum opponent sum is 9.

My program finds 5760 separate solutions, although we can appeal to symmetry to reduce these (e.g. requiring A < I, cuts it down by a factor of 2).