The simplest option is 1-13, 2-14, although we can certainly think about it further and possibly come up with something better.
And will the 6-7th place, which is vying for a spot, play against the 20th place, which is no longer in contention? Is that better? In any case, this contradicts the very idea of the Swiss system.
For the future, here's an idea: the same nine rounds of the Swiss system. Let's say we need to select 10 people. We make the top three places automatic qualifiers, and the places from 4 to 17 play tiebreaker matches in a BO3 format: 4-17, 5-16, 6-15, 7-14, 8-13, 9-12, 10-11. At least in theory, it looks good and doesn't contradict the idea of the Swiss system; it simply makes three places automatic qualifiers, and another 14 enter the tiebreaker zone. In theory, this should maintain motivation both for the chasing group – they need to get into the tiebreakers – and at the very top, where there is a fight for the top places.