But let's drive it down to just the question.

"IS there a way to have the appliacation hosted by us and our users accesssing while all along the data is being dtored locally to thier hardrive and shared through their LAN or WAN?"

The current app in a web browser does NOT demand a file share but could be a local file which is either by the local hard disk or network drive. The details must be finely ground here and must be driven by your spec.

So your application could be entirely on the web and the data local. For an example just look at any of those web based antivirus scanners.

The problem still remains that data can leak back to the hosts since your application is not open source and can't be vetted.
Bob