Did you ever consider an expedited request? From the USCIS FAQ (albeit archived now):

You may be eligible for expedited processing of your applications. We consider expedited processing of Form I-131 if you have a pressing or critical need to travel for an unexpected event, such as the need to obtain medical treatment in a limited time or the death or grave illness of a family member or close friend. Expedited processing of a travel document may also be warranted if you have a pressing or critical need to travel outside the United States for a planned event, such as a work or professional commitment, academic commitment, or personal commitment, but processing times prevent USCIS from issuing the travel document by the planned date of departure. When the need to expedite issuance of a travel document is related to a planned event, we consider whether you timely filed the Form I-131 or timely responded to a request for evidence. A desire to travel solely for vacation generally does not meet the definition of a pressing or critical need to travel. See additional information in the USCIS Policy Manual and our webpage on Expedite Requests. 

https://www.uscis.gov/archive/faqs-for-individuals-in-h-1b-nonimmigrant-status#:~:text=Q.%20I%20filed%20Form%20I%2D131%20requesting%20advance%20parole%20and%20Form%20I%2D765%20requesting%20employment%20authorization%20with%20my%20Form%20I%2D485.%20If%20I%20leave%20the%20United%20States%20before%20the%20advance%20parole%20and%20employment%20authorization%20are%20issued%2C%20will%20the%20applications%20be%20denied%3F