I seriously doubt Yahoo will restore your free email account from backups. And there's no way to put mail back onto a POP server other than to re-email it. You could send all your messages back out via a redirector. That will send the messages back to your email account without modifying the messages at all, including the envelopes. Mail servers along the way will modify them, but only to add headers you largely don't care about. The only problem with this is that the arrival time of the emails will be now. If you sort them by sent time, which may or may not already be your default, they should look exactly the same. Of course, they have to make it through Yahoo's spam filter, which might be a problem with the dates as off as they're likely to be.
Mail Redirector provides this feature as an extension to Thunderbird.