Have your thought of joining forces with bigger bakeries or other companies in the baking industry to expand your reach?
I have had lots of times when competitors (often larger than us) have tried to intimidate and threaten. Ultimately they see you as a threat which is a good thing but price cutting doesn't help unless you have deep pockets to whether the ongoing storm.
You need to set your prices based upon the value you see for your products and then offer service, service, and more service. Look for new ways to innovate and expect them to copy, keep innovating. Customers are smart and they can see what is going on and ultimately it will be the quality of the product and the service you provide that will keep them coming back. Also be careful not to be too open with your pricing..the more open you are the easier for someone to undercut.
Look for new ways to expand, just because your in a rural area doesn't mean you have to think rural unless you choose to.