Hey I was researching something like this yesterday and somehow missed this post, did it last night with a combination of Tasker, Foldersync and Autoremote.
In my implementation Foldersync handles the actual syncing to my google drive account, Tasker initiates a sync whenever the reading app is closed or it receives a message from another device that a change was uploaded and Autoremote to make Tasker on each device talk to each other (for example once I close the reading app on my tablet it initiates a sync and then sends a message to my phone to wait a couple of minutes and then initiate a sync there as well).
Does Dropsync detect changes in the cloud automaticaly? does it pull changes on a schedule? or does it detect changes on the device?