I'll flesh this idea a bit since you asked.
As a hierarchical structure, Cogs has five tiers:
Tier 1 (1 team)
Tier 2 (3)
Tier 3 (4)
Tier 4 (3)
Tier 5 (1)
A 12 team single elimination tournament would be four rounds. Four teams would be seeded into the quarterfinals (either based on last season's results or randomly). The non-seeded eight teams would play a round for the remaining four quarterfinals spots. The teams who get knocked out in that round would be placed into tiers 4 and 5.
The eight teams in the quarterfinals play, four move on to the semifinals and the four who lose get seeded into tier 3.
The four teams in the semifinals play, two move on the finals and the two who lose get seeded into tier 2.
The two remaining teams play in the finals, the winner gets tier 1, second place gets the A1 spot in tier 2, getting the first chance to fight for tier 1 again.
So while seeding into S3 this way may not be completely non-random, it would reduce the random variance significantly. Initial bracket seeds being based on last season would give the previous top finishers at least a tier 3 seed, but still require them to fight for a better one. One team in the bottom four would get the short end of the stick, but other than that the seeding would be entirely results-based.