Why don’t you just use American Express? If I have a merchant dispute and they don’t fix it after 1-2 emails. I just charge it back by calling AMEX. It works fantastically well.
More than likely, yes. Chargebacks work way better for goods than it does for services. The online store you bought goods from might ban you if you initiate a chargeback, but usually with stores it's not that big of a deal, there's an alternative store to go to anyway.
Why would you want to continue doing business with a company who put you through a “massive shitfight” over money owed to you? I would charge back and never do business with them again.