Not sure where the bug(or feature) is from your description. It could be your browser, the sublime video player, or something OS specific. If it really bothers you right now, you can just look at the page source and download the mp4 file directly, to play in perhaps another tool.

Your browser probably has some native plugin to play the video, so you can try watching the mp4 directly in that, which might identify if the full screen issue is the browser or the sublime video player part.

FWIW, it works sensibly on windows. It seems strange that Macs have such a problem with multiple monitors. My colleagues are always wasting 10-15min of every meeting trying to figure out how to attach the projector, or use the screen sharing tools(adobe connect) to share the right monitor.

It's OSX. From Lion onwards apple added a fullscreen API in the core OS, it's garbage (especially when using multiple monitors) and yet many softs which had previously implemented their own correctly-working fullscreen mode switched to it.

I really dislike the way OS X handled their full-screen stuff. If I knew how to turn it off - and I've googled around - I would. :/

alt + f (found that in the keyboard shortcuts from right clicking on the video) should maximize the video in the browser window.

Ah, that makes it fill the entire browser window - which is pretty close to what I want! Thank you!