So I locked the eye-bot inside the vault before getting the tape and have no prior save. Am I royally screwed? I can't open the vault from behind the ferns and if I open it anywhere else I get a speech from Mr. James Earl Jones.

This may be unlikely since you didn't get the tape, but did you happen to get the Buddha statue? The tape and note pieces are purely optional, but the statue is vital. If not I would recommend continue playing with a save from the EASY profile included with the game.

No, no statue either. That save won't have all my choices in it... sigh, there's no other way?