Broadcast Monitoring with Intensity Extreme

I'm trying to monitor through the Intensity Extreme in FCPX, on a Macbook Pro 15" Retina. If I use Thunderbolt directly from my computer to the Intensity, it will only let me go up to 720p. If I use the Thunderbolt through my external Apple Thunderbolt Monitor...I can get 1080p. But I'd like to be able to use broadcast monitoring without having to go through my Apple Monitor...as I use that thunderbolt for an external drive. Any advice?

I don't know if this is any help to you, but I'm using Intensity Pro HDMI output to a dinky Vizio monitor, and I get 1080p.

I don't know if this is any help to you, but I'm using Intensity Pro HDMI output to a dinky Vizio monitor, and I get 1080p.

can you display the video in full screen on a second monitor when you are in davinci?