Paul. I am a life-long sailor dealing with tides, so I have "some intuition how this works", just as you wish.

We agree that tidal "patterns aren't fixed on strictly periodic dates", for reasons I have partially listed. No I do not expect "some formula" here, nor even a "look-up table", or I would clearly ask for such.

I am trying to meet your exacting criteria not to "punt" nor "hand wave" here. Any very-experienced sailor can imagine an ENSO data buoy anchored in 9km of Sea picks up tidal noise, and knows that the Sea is quintessentially chaotic. That's actually where my line of thought comes from. Chaos Science is simply the formalization of what a good sailor knows.

All waves are orbital in phase-space.