Is there a way to control browser size and position across multiple displays / monitors?
Go with a chrome/firefox extension that has access to window/tabs specific APIs.Either embed your whole application in the extension or communicate with the extension through messages (chrome, there's an equivalent on firefox).
Support in Chrome is experimental.
You can use window.moveTo(-1000,100) to move a pop up to a second monitor in IE if you check the permission "allow script-initiated windows without size or position constraints" under Internet Options/Security/custom level.
If you only have a single monitor connected, it will move the window to the edge of the primary display. I have not found a way to do it in Chrome though, it doesn't appear to have the same security option.
Try using the chrome.windows API to interact with browser windows. You can use this API to create, modify, and rearrange windows in the browser.
https://developer.chrome.com/extensions/windows
It even works with nightwatch.