So it appears that the answer is that the bulges are a forcing function, not a displacement.

Am I the only one skeptical that Newton would confuse a force with a displacement? What am I missing?

Good point. I'd be curious if anyone actually has the text showing he said this. It's in principia I guess. My bet was that he never gave a full description, but rather just said that it is moon/sun that *causes* the tides.-- I'd wager he acknowledged the incompleteness of it. Which would still be mostly accurate. It's hard to imagine him knowing about the complicated tides in England and saying definitively he had a full model of the tides.