The change strongly biases faction selection towards those that play OK even when hemmed in. It is now very dangerous for first player to select a faction that plays badly when other factions are in play.
It also makes it near impossible for 4th player to choose a weaker faction, since the other factions won't have been bid up to take account of it.
On a more general point, I don't think changes that markedly alter things should be implemented without play testing. At least make both options available, and then revisit after the new version has been properly road-tested.
My preference (at least partly to speed the auction stage) would be for the option where factions are selected as at present, then everyone submits their maximum (relative) bid for each faction. The auction then proceeds as at present, but automatically. In turn, each player's bid is determined as maximising the difference between bid and the player's valuation.