Norway has substantial public media funding across the political spectrum, but as you point out it always comes with conditions, even is less so than the funding for the state owned broadcaster.

Combining the two models and putting public funds into several perpetual trusts intended to provide funding from their profits at arms length from any sitting government similar to the (private) trust funding The Guardian might be an interesting alternative.

(EDIT: Norway also has its own variation over The Guardian model - the second largest media group was founded by unions but is now majority owned by the combination of two public benefit trusts)