They have both a live chat & phone number. The phone number has been around a long time (I worked there from 2007-2011. We took customer service seriously. Except for the poorly conceived qwikster debacle, netflix was usually just ahead of amazon as #1 in customer service. Our policy was to refund that amount on the cancellation. And if I recall they would normally credit you anyway. Since I don't work there anymore, I am not defending them, I am just clarifying your misunderstanding.
In fact I googled for netflix call center and got: https://contactus.netflix.com/help
. At the bottom of the page is a live chat & phone number. both promise < 1 minute response. A lot less time than it took you to write this post.
It's interesting, having worked in companies like Yahoo, Netflix, PayPal, etc. A lot of evil is attributed to a company, when in fact the companies that I worked for were filled with people who would go out of their way to help a customer like you.
I would certainly call or do a chat and say you are very frustrated after all these years and the least they can do is refund the rest of your month. If they don't do it, I would be shocked. And if I can always ping my friends there to make it happen.