Take a look at Intensity https://www.blackmagic-design.com/products/intensity/. It has HDMI in and out and you should be able to just plug an HDMI cable from the card to the TV. Probably need to adjust a setting or two in FCP as well.
It was actually 720 23.976, but I tested 720 60i as well. Just did a test with a 1080 project and apparently it’s working as expected, but a bummer not being able to monitor/output from a 720 project.