Is the schismatic portion still considered "of the Church"?
I don't even know anymore. Ott's Fundamentals of Catholic Dogma would say "no" but it's not infallible, even though he takes its information from authoritative sources.
"Hunker down and pray" is the best advice I've ever received. That's why I don't fault sedevacantists or SSPX adherents for their positions, nothing makes sense right now.