I'm a little wary of doing that - presumably they'll start pushing back and getting on credit card shit lists is something that makes me feel even more helpless than not being able to cancel something.
Agreed with other comment. I used to work with credit card network. Chargebacks are a penalty for merchants, not consumers. In the case of a disputed charge, the worst that happens to the consumer is they do not get their money back. The merchant has to pay a fee no matter the outcome. It's used to force merchants to be as clear in their accounting practices as possible.
That's what this system is set up for. To protect YOU. Linkedin mislead you (allegedly) to believe there would be no recurring charge. They made it extremely difficult (currently impossible) to cancel these charges. Call your CC company and put a stop on all future charges. Your CC company will fight to help you. Remember CC companies make good money if you stick with them (a % of every sale goes to the CC company's pocket) so they want your business.