I already basically wrote this but I figured I'd make it more prominent here to help people out.
The trick is to be persistent and patient. If it gives you an error just keep trying over and over. EVENTUALLY you'll get it to work. This goes for every step of the process (accessing the page, purchasing points, buying the maps, etc). It fucking sucks and it's going to take you a while probably but eventually it works.
I'm currently at 60% in downloading the maps now and it's not giving me any trouble at the moment. The only thing I'm worried about is the update part once CoD4 is booted up since it's going to take longer to retry the download.
Hopefully this helps somebody.