Out of the question, it has no definition which is only related to physics. Well, there's the "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" definition, but this was chosen to match the celestial-based unit related to the Earth's rotation (which does not tell anything to extraterrestrials).

Don't need to. It's the hydrogen wavelength / pi.

Wouldn’t be required. Take any frequency, Hydrogen in this case, and multiply it by pi which is unitless. The resulting frequency is pi times whatever you started with no matter how you count the passage of time.

It's ruled out by the signal being modulated.

The question the choice is answering is where do you put a signal where other intelligent minds might look for it, yet which isn't at a frequency where the universe is particularly loud in ways that will make detecting your signal harder.