I vote for Caradhras acting out of its own malevolence, but with encouragement (of which it may or may not have been aware) by Sauron.
Agreed... It may not have been any kind of plan, per se... I don't think anyone (to quibble with our movie Saruman) would have intentionally guided the party to the path through Moria, and risk losing the Ring there. So I don't think Tolkien was telling us that...
This is possibly just general interference by bad things... like the Watcher in the Water and the Balrog. "There are older and fouler things than orcs in the deep places of the world".