If there is no other file-sync rule targeted to any of your device group(s) of interest,  the following possible is one possible way.   For EACH existing device group to be targeted, you need two file-sync rules, one alert rule, and a  newly created child device-group.

The first file-sync rule is for downloading the large file to the target device group.  The alert rule is triggered whenever a file-sync event  is reported, and the action is to relocate a device to the newly created child device-group.  Finally, the second file sync rule is for uploading the small file from device in the child device group, and a post-sync script to remove the big downloaded file whenever a successful upload sync of the small file is complete.  The content of the small file is immaterial and not tested.

If you have  other file-sync rule targeted to any of your device group(s) of interest,  you can use similar approach as above, but use custom data rather than the small file for the upload direction, and the alert rule triggered for particular value of the custom data collected.  Your device need software to write required value to an INI/XML file for data collection, rather than writing out the original small file for upload back to the server.

Unfortunately, I can't move the devices from their source folder. 

The move operation is done automatically by the server, and there shouldn't be any permission issue.  However, You do need permission to edit the required rules, and permission to create child device group node(s).