I had the same issue; no playback in full screen was working, did not matter which monitor I was working on, which format, sequence format, nor which monitor I set the preference too.
I finally found the solution! The hardware (by default, the button with the icon of two gears inside the timeline window) needed to be disabled. Now toggling Cmd + Shift + F keys works for whichever monitor I set the full playback mode.
Hope this helps as I did not see it as a potential solution for those still struggling to find an answer.
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Ian Levin
Film, Television, and Digital Video Editor