I've dealt with this quite a lot in the last couple years and what I do now is not engage with the supplier on their terms. I live in the UK though which has reasonably strong consumer protection laws so companies can't just take money from you without your permission. Also I don't think it's a coincidence that most of the companies I've had problems with weren't operating out of the UK.
My thinking is that I've signed up for something via a form on the web then I should be able to cancel the same way. If I've supplied a credit card to pay for the service via web then I should be able to remove that payment method via the web as well.
So if they say I have to cancel by calling them on the phone I won't do that anymore. I will instead just send an email to their customer service address informing them (rather than requesting) of my cancellation. I also specifically tell them that I withdraw my consent for them to charge my card (I don't actually know if this does anything). If they respond by telling me to contact them via phone I just tell them no.
I additionally sometimes cancel the card they have on file so they will be unable to charge me. If I have a direct debit in place (this is a UK thing) I just log into my online banking and cancel the direct debit.
I did recently have a case where my card was billed again because I didn't cancel the card and they justified it by saying their terms and conditions contain a 30 days notice to cancel (this was a b2b SaaS). I responded by reiterating that they didn't have my consent to charge the card they had on file and I then filed a chargeback with the bank and got the £400 back.