funny, the exact same thing happened to me in November, and I did the same thing, tried to extract the bottom piece out with reverse drill thingy. So I took the car to toyota and I do not have the bumper to bumper warranty but have a 100 mile powertrain warr. which is not original, only from some toyota dealers on used cars. well, supposedly the bolt is not covered by power train because it is a fastener, but after several conversations on the phone with the rep from the warranty company, I got them to pay. Total was 550$ and I paid 50 deductable.
Also, when to bring it in, dont tell them you know its in fact broke if you have a warranty cause they might find a way to void it for the tampering, which isnt actually legal. BUT if you are planning on paying, tell them right off you know its broke cause they will charge you more to first determine if its broke before removing valve cover.