Thank you for your advice. At first it didn't work - but after a few minutes and a few more attempts, it worked. The noticeable change was that TurboTax included an option for me to check a box to have my tax status texted to me. This was previously not showing at all, so I knew that the phone number switch worked when this new feature appeared.
I was able to use my US phone number from the free app called 2ndLine. I could verify it with the text verification as well.
Filing from Hong Kong :).
