Mag oxide will pass through as a laxative with low absorption. Mag citrate or theonate are good.

I get that click 2 out of three swallows. I never paid attention to it. Hope I don't now. I get a slight click on the left and a microsecond after, a loud squish then click in my right ear. My jaw does not have to move at all. Maybe my clicking TMJ has desensitized me to this sound.

But then, I have learn to ignore 60dB tinnitus. Ringing like a high pitched bell right now.

You might try finding a music track that has some sounds that can hide the clicking so you can sleep.