I'm not sure I understand this:
"The NTSC variations (~29.97, etc) are actually defined as 24 * 1000/1001 and 30 * 1000/1001, which are impossible to represent exactly in a way where 1 second is exact, so we don't bother - they'll be inexact in any circumstance."
The NTSC color subcarrier is exactly 315/88 MHz, so one could make the flick something like 1/528th of this period. The frame is related to the subcarrier by 525 lines by 455/2 color clocks.
See: https://en.wikipedia.org/wiki/Colorburst
So one NTSC frame is exactly 63063 flicks, one 30 Hz frame is exactly 63000 of them, one 24 Hz frame is 78750 of them and one second is exactly 1890000000 of them.