I found the following plot in the book Satellite Orbits; Models, Methods, Applications by Oliver Montenbruck and Eberhard Gill, Springer, 2000. The figure and description can also be found in google books. It's a low quality snapshot but it's hard to capture a dozen different dependencies over 20 orders of magnitude without showing the whole thing.
This answer points out that the orbit-perturbing effects of the Moon on a satellite in LEO are stronger than the orbit-perturbing effects of the changing Earth gravity field due to the Moon (and Sun, which I'd forgotten about).
After seeing the plot below, I realized that I'd also forgotten about the solid tide. And then I also noticed that there is no line for the ocean tide. I think these are different - incompressible water flows in order to make a tidal bulge, but can we think of the solid tide similarly - as flowing magma? Does the crustal shell outside just flex and bend to accommodate it? Does the crust significantly restrict it?
Any idea why ocean tide is not shown, is it's effect on Earth's gravity field so much lower than the solid tide that it wouldn't show up on this twenty orders of magnitude plot?
I also notices that the plot for the Dynamic Solid Tide parallels the two $J_2$ lines about four orders of magnitude lower than $J_{2,0}$ (looks like a $1/r^4$ slope). Does that reflect the relative amplitudes of the Earth's dynamic and static bulges?