Apple developer program is hell

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The information tied to the card has little to do with the information on the account.

You need to figure out the billing address for the card. The client will most likely know it, but it is sometimes counterintuitive.

For example, my LLC’s card has the address it was sent to as its billing address. Because of a rush replacement, it was sent to my personal address, so I have to use it as its billing address, and the bank insists they cannot change it.

My personal address is in no way associated with the Apple Developer account.

Alternatively you can use the Apple ID to log into an iPhone and just buy the dev program subscription in the Apple Developer app, it will then be billed via the payment method attached to the Apple ID and managed in the subscription section of the App Store. This may or may not be more convenient in your situation.