For anyone ending up here; I bit the bullet and decided to create the column myself, hidden.
Only, that also seems to not be possible. The API docs certainly do not mention that anywhere, and there’s this thread:
So there isn’t even a way to do this in a friendly way.
The only way you can sync is indeed to tell the user to please create a column with such and such properties, not set any option on it, not set a formula, name it such and such so we can find it (or name it as they wish and make sure to select it correctly when back, lest we overwrite a column they need), and then come back and continue the process. And to please make sure to not touch the column in the future.
Again I’m sure there are good technical reasons for those weird omissions, but they are very limiting.