I just did a large plate like this last week.
I cleaned the chuck face and the part well with alcohol, and used double faced tape.
After pressing the part against the chuck face with the tailstock for a few minutes, i was able to back the center off to face the first inch or so, then move the center back up against the part and complete the facing.
This way you can face the entire part. The tape also helps to prevent slippage so you can use less tailstock pressure to avoid warping thin parts.
Scott