How to export source information from Geni

You can try using the API for getting info on documents: https://www.geni.com/platform/developer/help/api?path=document&version=1

For exporting the GEDCOM export does add some source information so that is probably easier.
For info that is missing from the GEDCOM (info not exported) that you added yourself you might want to look at https://www.geni.com/account_settings/download_activity. But it will take a lot of effort to combine the info.

A GEDCOM is limited in the number of profiles you can export, but you can do multiple exports (from different profiles). There are the ancestor an descendant reports that may be useful to find profiles for an GEDCOM export. But please remember that you can only export a GEDCOM from a profile you created yourself. You can export from multiple profiles but you would need a program to join those GEDCOM files (there will probably be duplicates)

You can probably get the information you want, but it will take a lot of effort.