How to integrate partial version control, data exchange and research assistants?
I've run into similar problems in collaboration with biologists, and found that a two-technology approach is best.  


Large-scale experimental data is shared via one or more BitTorrent Sync folders.  The experimentalists can just drop their files into the appropriate place in the folder, and they get synchronized with the server and everybody else's copy (like DropBox, but private, free, and unlimited size).
The analytical tool-chain, research products, write-ups, etc. are maintained in your preferred version system (e.g., git).  This is then integrated with the experimental data just by giving a pointer to the appropriate directories.


This has the advantage of maintaining the data separation that you need, keeping the scary version control software away from the experimentalists, and also avoiding juggling massive globs of data in a version control system that was never intended to support this.