Operating as a profitable non-profit foundation with no owners, where all profits are reinvested into the project

Neither myself nor Hannah own any shares, assets, domains, trademarks, or other companies related to Ghost. Everything is owned by the Foundation.

our intention is to expand the seats on Ghost's board of trustees beyond myself and Hannah.

I don’t see how this is fundamentally different from the WP Foundation approach. It still depends on people who despite claiming an intention haven’t given up control.