Also, this noise doesn't sound like a typical ground loop hum which I am VERY familiar with unfortunately
AC hum is not the only thing that can present in a ground loop. A ground loop could also be a path for this clicking into your audio component(s) -- but, the fact that this clicking is audible, is really puzzling!!
Nope. No diodes across the coils.
I would say you've been lucky. The diodes are really important.
Try shorting out the 100Ω resistors (either all at once, or one by one) and see if that either quiets the audible clicking or, at least, removes it from the audio signal. Especially R6, which really looks like it should be on the other side of C2. In most cases there is no need for such a resistors. Only needed if noise reduction is an extreme requirement -- and inductors are a better choice. The regulator already does a bang-up job of reducing noise.