If anyone else has this problem, check out http://www.unlockit.co.nz/ from your iPhone. It creates APN settings profiles which can be installed even if your carrier has disabled them.
Their site simply constructs the same kind of configuration file that Apple's official iPhone Configuration Utility generates. You can override an APN in those configuration files...the internet APN, and ONLY the internet APN. There is simply no place in the iPhone Configuration Utility to specify an MMS APN, and there is presumably no field in the configuration file itself for it to go.
iPhone Configuration Utility, unlockit.co.nz, and all their ilk ONLY fix internet data, and not MMS.