Regardless of whether or not it was user error, the billing system has two REALLY bad things going for it:

1) It's not accepted in certain international countries. This needs to be addressed IMMEDIATELY.
2) The billing user interface is convoluted. I figured it out after clicking around and reading stuff, but that's the problem with the billing user interface. IT SHOULD NOT BE DIFFICULT TO GIVE SQUARE YOUR MONEY. Whether these extraneous charges the OP got was due to user error (which is entirely possible because of the convoluted system) OR due to a billing system that's placing erroneous charges, this also needs to be addressed.

The amount of menus that you have to dig through for billing is ridiculous, and Square splitting up the "basic" fee from the "character" fee makes it even worse. Like I've said before, I get a feeling whatever team was responsible for the horrible FFXIV UI was partially responsible for the design of the billing system - navigating through these menus reminds me of launch day XIV where you had to dig through hordes of menus just to get one thing done.

Anyway OP, I think a last ditch effort is to speak to a manager when you talk to their CSRs - if the manager can't help, then yeah, get your credit card company's help and dispute the charges. Two threads talking about the exact same thing happening made me double check my credit card account in fear of getting hit by these charges myself.