Product: Credit card or prepaid card

This complaint is filed against Banana Republic store credit card, issued by Synchrony Bank under a XXXX logo. For my current billing statement I scheduled a payment for XX/XX/2021 in the amount of {$630.00} only to realize that past the current billing cycle there was an additional small charge, so instead of having to make a second payment later on I decided to adjust/change my original payment from {$630.00} to {$650.00}. 
Something went wrong with the edit payment functionality on the credit card companys side, as I was surprised to receive on XX/XX/ two email notifications from Banana Republic indicating that two payments were taken from my checking account, on the same exact date ( XX/XX/ ). One for {$630.00} and one for {$650.00}. When I checked online, the credit card company showed both payments and a negative balance of {$630.00} ( credit in my favor ). 
In order to get reimbursed for the double charge/payment, on XX/XX/ I called the customer service number for the credit card company and asked to be reimbursed. The only solution offered was to wait for a reinbursement check to be issued and mailed via USPS to my address in 3 weeks. As an alternative, to avoid the likely scenario of the check getting lost or delayed in the mail during the holiday season I asked for the check to be mailed sooner, similar to the overnight shipping used to mail Banana Republic products, but I was told that this is not possible. I also asked if I could get my money sooner via a cash advance and for that I was told that I would be able to withdraw money in cash from a bank near me but that I will be charged a 5 % fee for a cash advance, even though the {$630.00} is actually my own money and not a real cash advance against the credit line. 
Disappointed with the options provided, I filed a customer complained with the credit card company to voice my concerns over the fact that the double payment should not have taken place in the first place and for the fact that issuing checks in three weeks and charging a 5 % fee to recover the funds via a cash advance is abusive given that funds belong to me, not the credit card company. The complaint ID I was given is XXXX and when I asked when should I expect a resolution to my complaint I was told that the company does not send written responses/resolutions to customer complaints. 
I find the whole situation weird and at on the border of financial abuse, as : 1. The credit card company should not have charged me more than what I owed ( {$650.00} ) in the first place. With all my credit card payments ( with other companies ) the credit card website is build such that overpayments are not even possible. So to even allow this type of overpayment is a problem in itself in my view and should be fixed.

2. Given the charging error on the credit card companys side, which I reported as soon as I was made aware of It ( on XX/XX/XXXX ), the credit card company should have been able to cancel the double payment from their side. I was told that the credit card company does not have this ability. 
3. Additionally, when using the alternative of the cash advance to recover my own funds ( {$630.00} ), I find it abusive to have to pay a 5 % fee, when in this case, I am only withdrawing my own money and Im not using the credit line.

4. Lastly, I find it unacceptable that this credit card company would not provide resolutions/responses to their customer complaints. What is the point of a customer complaint if a resolution is never provided? 
For all these reasons I hope that your institution will look into the practices of this credit card company to ensure that measures are taken to correct their behavior. 
I attached below evidence of the credit owed to me and the two different emails confirming the two payments on the same date ( XX/XX/ ).