VaguelyJay There is no way to remove the packs from the old account, but support does have two options. One is to help you recover that old account, if you know enough details about it. The other is to accept your proof of ownership and add the games to your own account. These might be the same process on the back end; I wouldn't know.
Point is, take a photo for each pack showing the disc, its case, and the product code (clearly readable). You can upload these photos when you submit the help request.
I would strongly recommend using live chat rather than email. If you don't see the option, try this link:
https://help.ea.com/en/help-contact-us/?product=the-sims-3&topic=missing-game&category=manage-my-account&subcategory=find-missing-game
You could also try entering any email address you currently have access to into an EA login window (like the one on this site) and clicking "Forgot your password?" If the address is associated with an EA account, you should receive a password-recovery email. Check the spam filter as well as the inbox. If you can show you own that account, and having access to the linked email is enough, support should be able to merge the accounts for you.