The only way to get the free trial multiple times is to call and cancel BEFORE the free trial expires. Since according to your previous posts it already expired, the only way to get it is to pay for it. Officially you're not even supposed to get trial multiple times, but a known loophole that has yet to be closed allows you to get it again via DirecTV's website, if you cancel before the trial expires.
All sevices on the account, whether charged or free, will expire on their own. Even if you remove the HD Extra pack 3 month trial, the line item will remain on the account until the promotional line item expires on the account. This would have no effect on getting the offer again. No idea who he is talking to, but I don't see any reason why the option would not have populated. Most offers have an expiration date much longer than the offer date. Originally, the HD Extra pack's offer date was the same as the expiration date, which is why you could remove it and immediately add it back at no charge. They may have fixed that. If the OP had the 6 month promotion that cancels on it's own, the expiration date may be 3 months longer than the offer end date. I'm baffled as to how a CSR couldn't find this information.