Thanks EitanBlumin for your feedback. It's great to have these ideas and suggestions to improve our products and first of all, my apologies for my mistake about the syntax, I already fixed it.
As we cannot consider use SqlPackage or Export/Import service as a backup mechanism, the best practice is to perform a database restore using PITR at the moment that you want to export.
Being said this, the next step, when you have this database restored, is to proceed with the deletion of these unresolve references calling DeployMyExternalTable stored procedure to delete all the synonyms or external tables including the references (for, example, views), export the data and after it recreate again this if needed.
I used synonyms as an example and I agree with you about the idea to include the option for the "VerifyExtraction=False" parameter for the "Export" action as well and not just the "Extract" action, our Azure Product Team is aware about it and I would like to suggest if you could add this idea in our feedback website we have others about the topic of Export/Import. I submitted this feedback internally to our Azure Product Team.
Meanwhile, the main idea to export the data without receiving this error currently, having in just only place of this logic. All this feedback is very welcome, please, continue this discussion adding your ideas or suggestions about this topic, I'm sure that your experience could help the community.
Thanks again!