Retooled Browser Player Page or Responsive Layout.
It would be super helpful to be able to split a 1080 monitor with the player. Unfortunately the page has hard widths of 960px. The player page could easily be adjusted to have a min-width of 816px thereby permitting it to be 1/2 the width of a 1080p monitor.
Apart from this, the whole site could be made responsive and that would solve the problem at it's core. Hollar if you need some help. :p
This is planned.