I hope this message finds you well, present circumstances excluded. My name is XXXXX XXXXX I am an attorney with over 10 years experience in handling litigation matters, including representing and suing insurance companies. It is a pleasure to work with you on this matter.
If the insurance company is unwilling to budge and handle this issue (as they clearly should), you are going to have to use a procedural mechanism called impleader, in which you as a defendant effectively sue and bring your former insurance carrier into the suit as a third party.
In that case, you have to file an answer to the law suit against you, but you also file a separate document impleading the former insurer and claiming that they are actually the entity to which liability must rest. Based on your documentation and the common understanding that they were to insure through that last 24 hour constituting the say of October 17, 2012, I think you have a very good shot at shifting the liability, if there is any, to the insurance company and having your attorney costs covered in the process as they would have otherwise been responsible for those attorney fees or providing adequate representation.
Under the circumstances, that is your best, XXXXX XXXXX only option unless you can convince them to accept coverage by the threat of impleading them into the case.
Let me know if you have any additional questions or comments.
Best wishes going forward!