There is an endpoint available for you to publish a workflow to a private studio using information found at the following link: https://help.alteryx.com/current/server/workflows-admin-interface#workflow-migration. The details can be found under Migrate Workflows and Step 3. You will need to set the owner to the email address of the user that is trying to upload it, at which point, it should go to that user's private studio. Keep in mind this will need to be run from the admin side.
If you do encounter issues after using the API to upload your workflow please reach out to support@alteryx.com and we will be happy to help.
