How to screen record higher than 1920x1080
A quick Google search found one of my favorite tips for OS X: http://hints.macworld.com/article.php?story=20131030130206132

Essentially, go to System Preferences > Displays, option-click the Scaled button, then select a  new resolution. Your QuickTime movie should record at the new resolution, but remember bigger resolutions take up more graphics power.