As I understand it, you would have to switch to Business Class Service through Time Warner Cable. I'm sure there is a fee involved, and likely a change in the cost of your monthly service. This would be the direct answer for how to get your ISP to give you a Static IP address.
DynDNS is a solution if (and only if) the firewall you are talking about does a reverse lookup to find the name of the domain the source IP address is in (your public IP address in this case), instead of the IP address itself. You stated your concern was based entirely on the IP address, not the domain name. I suspect DynDNS will be of little use in this scenario. I suspect this because although your IP address changes from time to time, your domain does not (if you are even part of one) when using DHCP (dynamic IP addressing) through Time Warner Cable.