From what I understand, you're trying to get carrier calculated shipping added to your account, is that correct? If you don't require the features of the Advanced plan (other than carrier calculated shipping) there are a couple other options for you!
One option is upgrading to an annual plan, on any annual plan carrier calculated shipping is free. However, as you mentioned you're only selling for a couple weeks of the year, this likely won't make sense.
The third option, is getting carrier calculated shipping manually added to your account for $20 USD per month. This can be added to any subscription plan (including the Basic plan), and from what you've described is likely your best option!
In order to do this, you'll need to reach out to our Shopify Support team directly - as they'll need to manually add this option onto your account from the back end. You can also change your subscription back to the Basic plan if you no longer require the Shopify plan. If you do this, as soon as you make the change you'll receive a prorated credit for the difference in plan prices.
Let us know if you have any further questions!
Hilary | Community Moderator @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog