Alternative to Upload Center/OneDrive for syncing SharePoint with local server?

Hi, here's the setup: 
A single Server 2012 R1 machine in an office with 13 workstations and a remote office (via VPN) with 3 machines. Server roles are DC, DNS, file share.

We recently signed up for Office 365 E1 for Nonprofits, and I'm planning on migrating our office file share to SharePoint Online so our users can access it from anywhere.  I've already set up a test, which seems to work.  The problem is, I'd like users to have the performance of a local share when they're in the office, which is most of the time.  The first thing I tried was using OneDrive and the Upload Center to sync the local file share with our SP online library.  So far, it's been a disaster.  I've already written about the issue with bad characters in filenames, but the upload center is slowing the server down and continually running into problems with the file cache needing to be repaired, and none of the fixes I've tried have lasted for very long.

I'm going to map a drive on the workstations to our online SP library, but I'm wondering if it's possible to map a folder to a share on the server which is synced with our SP library.  In other words, as an alternative to using the Upload Center/OneDrive to sync our local share to SharePoint, instead having the server sync a local folder from the SP library, with the SP library being the master. 

One thing I tried was mapping a drive on the local server to the SP library, and then sharing it on the network, but it doesn't work.  Even symbolic links to it won't work, and junctions require a local volume.

Should I just give up on keeping a local mirror of our files?  That seems to be the model MS wants us to use. But I'm concerned that when we switch over, our users will completely overwhelm our (lousy Comcast cable) internet connection.