SharePoint 2013 OnLine: Improve timing to copy one document set to another library

Is there another way to immediately move or copy a document set to another library in a another site?

Here is what I have done:

1. Created send to locations in SharePoint Admin Records Management using the service: /_vti_bin/officialfile.asmx
2. Enabled Content Organizer in both libraries and added specific content type to drop off library in target site as well as target library
3. Created rule in target site to send specified content type to target library
4. Process:
   Create document set in originating library
   When document set is ready, select it and sent to other location
   The document set is then zipped and sent to the drop off library in target site
   Overnight the document set is successfully moved to target library

Problem: I can't wait that long. Once document set is ready and the move initiated, I need it to arrive in the target library.

Is there another way to achieve the same result without the time delay?

Any guidance would be greatly appreciated. I am not a developer. Thank you.