Well I mean.... there's your problem right there. You're paying for a 12 hour response time, on a plan the AWS has told you fairly explicitly is NOT for production or mission critical workloads.

I get that it's frustrating that they try and nickel and dime you on support costs, but at the end of the day you do get what you pay for. I've used Business and Enterprise support in the past and always had very good support from them delivered very quickly.

I'd start by going to business plan and trying again.