You can file a writ, but its acceptance is at the discretion of the reviewing court. Since you waived time, it's going to be difficult to argue that you've suffered any prejudice from the behavior of the trial court. Yes, the court made an error, but you'll need to argue that it is one that has caused you harm. I'm not really sure how you would show that.

The forms are APP-150-INFO and APP-151. Be sure to read everything in APP-150-INFO before filling out your APP-151.