Can I engineer which couples end up forming after the final mission? If so how?

As you've likely already guessed, under the hood of the support ranks displayed in game, there's a numerical score for every support bond. What's not especially clear, is that, once you've reached the highest rank between two characters, this score can keep going up. Pairings at end game appear to be determined by this support value, rather than any particular narrative priority, or by the order in which various pairings reach max rank.

So, yes, you ought to be able to manipulate these results by grinding out support bonds between two characters in combat, or through meal sharing, etc. on exploration days at the monastery.