I finally (I think) figured out what to do in this situation. Here's what you need to do:
1. Fill out your whole tax return like normal, let TT do its calculations
2. Once everything is complete, go into Forms mode and on Schedule SE, line 5 apply an override and remove the SE tax
3. Call National Insurance, tell them your situation and that you are seeking a Certificate of Coverage. They seemed to understand this request fine and forwarded me to the International Caseworker department
4. Once you eventually get this (I am still waiting for mine), print out your tax return and mail it in along with a copy of the certificate
E-filing will not work with this process, you need to mail in a paper return with the certificate.
Some assistance from TurboTax for this scenario in future releases would be greatly appreciated.
