I know you have to claim everything else first, which is why I want to claim it now so it won't get bogged down under the year of mythicals Mystery Gifts.Sadly not really. Streetpass is the only way now, and even then you have to redeem all other Mystery Gifts before getting it from the Delivery Girl since it doesn't appear in the card album.
Is there a way to Streetpass between two games one system or emulate Streetpass in some capacity?