So you essentially need the same one ccmerged file to be present while you install all your premium content. This file has a record of all the store premium content you've installed, and that content won't work without the file. Now go into DCBackup inside your old Sims 3 folder, copy ccmerged.package, and paste it into DCBackup in your new folder. Go into DCBackup and delete ccmerged.package.
Open the launcher to create another clean folder, but this time, don't install anything yet. Then move the folder out of Documents\Electronic Arts again. world files in InstalledWorlds as well, if it doesn't happen automatically. Move the old one back into Documents\Electronic Arts, and use the launcher to uninstall all the store worlds that haven't been working. Trash the new Sims 3 folder you've created, the one into which you've been installing store worlds. The instructions are mostly the same, with an extra step, so I'm going to add that and just c/p the rest of the instructions, while (hopefully) changing all the tiny details that matter. Yeah, that's why I asked-there's a bit more work involved, but it's not so difficult.
