Do you use Stripe's risk evaluation API? In my experience, a lot of chargebacks come from people who have had their credit card info stolen, then file a chargeback when they see the unknown transactions in their statement.
You could also try using the two step auth and capture method to allow more time for the victim to realize their info was stolen and do an additional fraud check with potentially more up-to-date models right before performing the capture.
I did a study on leveraging machine learning to predict chargebacks and will be speaking on it here: https://conf.splunk.com/
If you have enough data (clean transactions and transactions marked as chargebacks) - and willing to do private study - I'd be happy to help (no cost).
Add an area on your cancelation page that offers for them to email you directly with any problems or if they need assistance cancelling their account.
Below that something add something like:
Unhappy with your subscription? Contact us and we'll make things right. We will assist you with cancelling your subscription and refunding your two previous payments.
Can you adjust something in your service so people can't jump in, use it, then never need it again? I don't mean to assume this is what is going on, but I imagine some people may try to get their $ back if they just needed a web tool for a one-off task.
Make it possible to cancel online and retroactively give refunds on your website. You'll never see a chargeback again.
You can do everything right and almost always lose. Sorry, just consider it cost of accepting credit cards. :-( Perhaps do an analytics on those that initiated a chargeback to see if you can detect a pattern and then watch out for that pattern and offer to have folks cancel their accounts.
Let's say people sign up, never use your service then file for a chargeback. You can contact everyone that signed up and don't use the service and tell them to cancel since they are not using it. You have to do the math. Will you be losing more money by doing that or by CB fees?