Well, aside from the factually correct but generally unhelpful "we don't know?"
The Clans do not use double-elimination or round robin tournaments for anything. All Trials, for Position, Bloodright, or whatever else, are winner-takes-all.
As with the Cloud Cobras, some Clans, probably the Wardens, would have deliberately thrown the bidding and avoided the trials entirely. Given that seven Clans wound up in the Sphere, I would expect somewhere between ten and fourteen of the remaining 17 Clans to have been involved in the battle round(s), with one round fought to determine who the Invaders would be and a second round fought by the winners to determine corridors. At the same time as that second round, the losers of the first may have had a go at obtaining a reserve slot, which apparently the Vipers occupied.
I would expect that the forces dispatched would have come from the Clans' most elite Cluster or Keshik, and to have been no more than a Cluster in size at most. Probably on the order of two Binaries or Trinaries, really.