If I were in your shoes I'd spend a couple hundred bucks to run this past an attorney that deals with insurance.
IANAL but I imagine that since the event occurred while you were covered, they can't NOT resolve that claim. Lawsuits can drag on for years, and if the way to avoid that was to cancel coverage (LOL) that would never happen. The neighbor's lawyer isn't going to bother suing YOU unless you are rich. But insurance companies (the people that work at them anyway) don't always deal with customers ethically and they may try to get you to agree to something that you have no legal obligation to accept etc. They are not looking out for you, they are looking out for their bottom line.
You should probably find new coverage on your own. Your loan servicer WILL do it but it might be way more expensive and the coverage will be what's beneficial to them, not you. Once you get a policy lined up call them and tell them you're switching insurance companies and see how they handle it.
Good luck. Sucky situation but you'll get through it.