I think many people have been conditioned to assume that replying to automated messages goes straight to /dev/null. Have you considered putting a link to a page that provides a quick cancellation workflow?
Here's one of those invoice mails in its entirety. Sent from (and reply-to) info@twiddla.com. See if you can figure out how to go about cancelling your subscription or getting a refund:
Your Twiddla Bill for April 4, 2019 to May 4, 2019
Hey, we wanted to let you know that on May 4, 2019 we charged your credit card $14.00 for your monthly Twiddla Pro subscription.
You can find additional information regarding your bill, individual charges, and your account history by logging into your your account at https://www.twiddla.com/ and navigating to your "My Account" page. You can also make changes to your subscription or cancel it altogether from that page.
If you have any questions regarding this charge, or would like to yell at us until we refund it, please contact us at info@twiddla.com.
I have no desire to yell at you, simply to cancel the account and request a refund. While sending an email is okay, it would be better if there was a link directly to a page to do so, just like unsubscribing from an email list. Regardless, I would recommend changing the wording from "yell" because that sounds hostile, and most people don't want the conflict.
One nice thing about running your own business is that you can develop your own "voice" throughout the copy on your site and in your communication with users. And that that voice need not be soulless nor corporate nor cleared by Legal.
Plenty of people have taken me up on the offer for a refund, and none of them felt the need to "yell", so I think they got the correct vibe. All our site copy and mails have this same casual, friendly tone. People seem to like it.
The people who did end up writing in are not your problem though, are they? It's the ones who don't. I wouldn't base my experience on the ones who cooperated.
Casual tone is one thing (a good thing), but I posit that an actually angry customer will not respond well to this.
"Oh damn I get this email again... and they are telling me I can cancel, but I think I already cancelled... wth. Hmm, maybe they'll give me a refund."
Now at that point whether the customer is right or wrong they'll read the yell part and think that you are mocking their potential interest in demanding a refund.
Maybe I am totally alone here (with the other guy I guess), but while I wouldn't go dispute a charge myself that wording of yours would not encourage me to write in and get my hopes up you are happy to accomodate me.
I understand wanting to have your own style. I am not opposed to the casual tone. You were complaining that some customers don't take you up on the offer, and instead contact their banks to request a charge back. I was suggesting that changing that one word (but not necessarily the casual tone) might make a difference in encouraging some of those people. But it is your business, you can try the suggestion or not, I apologize if my comment came across as pushy or anything like that.