@frozenorangejuic and @KNKV10 Honestly, I'm not sure what else to suggest. I borrowed someone else's computer a week ago and was able to reproduce the error, and then I consistently fixed it with the workaround I described. But of course there could be more than one cause of the issue. The laptop I was using had never had a TS3 install, and there were no extra game files or registry entries (and I checked for both when I was done as well). I did clear Origin's cache once, before I figured out how to force the broken downloads. But I didn't have to fiddle with the other Origin options (like safe mode downloads or a metered connection), or any other approach besides the ones I've mentioned.
It's not that I expect any of that to help; it's just a long way of saying that I don't know what else to do, either. This issue has been around for months, and a couple of approaches have worked temporarily, but (as you've seen) there's no true fix yet. Until EA offers one, we're stuck trying whatever we can think of and hoping we stumble on something that helps.
I want you to know that I've been sending this information along to the CMs, not that they're the ones who would be able to fix the issue. But I'll continue to bug whoever I can find until there's a fix. I'm sorry I can't do more, and I wish I had some better ideas to pass along. I appreciate your reporting back that nothing has worked, and I want to especially thank @KNKV10 for your persistence and willingness to try every potential workaround I've suggested. I do believe it's helpful, although of course I won't know until there's an official fix.
Anyway, I really wish I could help more, and as soon as I have anything, I'll be sure to let you know.
The downloading issue has been fixed by the latest Origin patch, released this week. You can read the patch notes here.
If anyone updates Origin and still can't download a missing pack, please clear Origin's cache and try again.
@KNKV10 Try clearing Origin's cache again, and if that doesn't work, uninstalling Origin the hard way. (I know it didn't help before, but perhaps this time will be different. Hopefully.)
Otherwise, I don't really have any suggestions, other than turning automatic game updates on, repairing the game in Origin, quitting, and seeing if the packs start auto downloading. Tomorrow, I'll forward this to the EA community manager who oversaw the issue.