It will suck if Cox buckles because they have a monopoly here there really is no other provider in the area.
the best solution would be then to check your local legislation and talk to a real actual lawyer
depending on the situation and the country, the only provider blocking a website could be weaseled and written into a refusal of universal service and a judge could order them to unblock the website and make them pay for your lawyer
afaik, however, idk if there is precedent for a court decision regarding websites. It could be compared to a phone company refusing to allow you to make calls to a certain number because they dislike the owner or a postal service not delivering to a certain address because they don't like the person who lives there.
idk if it would stick but imho worth a try
links below to what is the notion of 'universal service':