Yes you should check out lots of other banks. After all, you're paying them nothing right now, so you're worth more than zero if they sign you up as a customer. You should check out a mortgage broker, who could give mucho assistance.
If that path fails, you should actually stop paying your mortgage, not just tell them. After it's late, tell them there will be no more payments unless you can refinance at a lower rate. Don't do it unless you're serious about walking away. If you do walk away you'll save a boatload of money of course, and the worst hit to your credit rating will last 3 years tops. But you shouldn't need credit during that time, due to the savings. You'll be mortgage-free rent-free for at least a year, or two if you take steps to drag it out. Let Wells Fargo know that you know that.