Outlook uses the CFSTR_FILECONTENTS and CFSTR_FILEDESCRIPTOR formats that many applications do not understand. My solution for this problem uses an Outlook Add-in to intercept the D&D and convert the proprietary format into a usual file drop (CF_HDROP).
The Add-in replaces the DoDragDrop function pointer in the import table of OLE32.DLL with a wrapper function (inside Outlook's memory address space). The wrapper converts the D&D data and calls the original function.
This article describes how to hook into an import table. Outlook's D&D stream format is explained here. The stream data has to be written into (temp) files in order to provide a simple CF_HDROP.