I agree that there are many possible adventures to be had, each with their own circumstances and drawbacks.
I don't think an Elector Count of the Empire controls the Empire as an institution, they control their individual province. So we'd indeed not want to let Sigmarism florish in the Schattenwald, or the army that goes to reclaim it, but we already have a track record of not recruiting from Sigmarite groups for military support and I believe the area's said to be largely populated by Hedgewise, so it would depend on if the people there are Sigmarites and want to institute His worship.
Come to think of it, that trait probably does mean that we'd want to vote against everything that the Grand Theogonist votes for, but I think we'd be doing that anyways given the relations between the Sigmarites and the Colleges.