Re: Your paragraph which begins with "As with the Earth:". I think perhaps you confuse the three dimensional integration of gravitational force where a solid body (planet, moon, or star) is divided into layers and those layers into ...
Yes; plain language is horribly imprecise. I'll also admit it's been a while since I worked problems with the various field equations directly.
The one "out" that I will claim, is to reference the actual things in question: if you want a technical definition of Ampere's or Gauss's law, there are far, FAR better places to find it than from informal forum posts. Please don't take my word for it, or yours or anyone else's here, for gods' sake...

Wikipedia is a surprisingly good start on these most well known of laws/theorems, and once one understands the underlying math, the conditions and edge cases will also be apparent (which I glossed over intentionally).
I suppose the one failing is I should've made this "out" more explicit.

Now, the magnetic flux (field strength) in a closed path surrounding a conductor. I think it is important to differentiate between two types of closed paths that can surround a conductor with a DC current. One such closed path would be the classical path of equal field strength. This is what we envision when we see the classic pattern of iron filings on a piece of paper that the conductor passes through and which are called by the simplistic phrase "magnetic lines of force". This type of path is, by definition a path of uniform field strength.
If you'll permit this one indulgence -- strength is "line" density, not the path itself.
I never liked the idea of "magnetic lines of force" anyway. There's no such thing as a line, you can't count them (no matter how much a certain cgs system wished it were the case

). It's terribly hard to work with (have you ever tried deriving actual field line curves?!), and leads to a lot of easy mistakes -- perhaps another illustrative example has happened here.
The only thing they have going for them, I suppose, is exactly that, the intuition from metal filings. I suppose it's the more interesting of the effects that are easily observed from such an experiment; but the more meaningful observation really should simply be that more filings are attracted to the poles, where field strength is higher. Alas, we can't change history, only learn from it.
Another poor example for lines, is spinning a magnet on its axis: this does absolutely nothing, as it happens -- but if you are imagining a bundle of lines trapped in it, surely they must be twisted up by the motion, right?
"So, too, the magnetic field around a wire, at a given distance from center, is independent of the wire diameter, so long as the wire radius is smaller." I fear that you did not express whatever you wished to say very well. The radius of the wire is always smaller than the diameter.
Too many pronouns, sure.
To be clear, by "independent of wire diameter", I mean, has no dependency on it -- it doesn't matter that it's the diameter or radius, there's no proportion, the factor of 2 is irrelevant. And the wire radius must be smaller in relation to the radius of the curve, because obviously if some current is outside the loop you're checking, it's not enclosed, so you'll be missing that amount, and now the geometry and relative dimensions matter.
Moving charges, which constitute an electrical current, will be subject to electrostatic attraction and repulsion. In the case of a current, these charges are usually all the same polarity and will therefore repel each other. Therefore, even a DC current flowing in a solid conductor will, to some extent, exist as a stronger current near the surface of that conductor and as a weaker one at it's center.
Not quite. There is no imbalance of charge -- the wire is a mass of ions (atoms sans some electrons) bathed in an electron gas (the remaining electrons, such as to make the total charge neutral, of course).
Give or take exactly which electrons you assign as "gassy", i.e., how "ionized" the atoms are.
For which there are theoretical derivations, if it really matters. Which, it certainly does for the study of semiconductors, but suffice it to say for present purposes, metals are full of electrons, while being extremely neutral overall.
There is a surface layer, associated with ambient electric fields; metals are polarizable. Since surface charge is supplied from the abundant bulk, this change occurs rapidly (essentially speed of light*). The DC field due to current flow in a conductor, is extremely small (mV/mm if you're pushing it hard?) so there is essentially negligible change in the surface distribution of charges; and anyway, that change only occurs once, so amounts to exactly zero DC current flow. Also, the charge density at the surface versus the bulk, is essentially identical; the electron concentration is mind-numbingly vast in metals, and literally a handful of extra electrons at the surface, amounts to nothing.
*If you're applying a fast enough varying electric field that AC effects matter, then you can draw the equivalent circuit and that suffices for analysis: namely, there is some displacement current due to the varying electric field, which in turn draws a current through the metal, which at AC, largely occurs at the surface due to the shielding effect of self-induction (skin effect).
Note that the EM skin effect is a depth corresponding to frequency and material properties, whereas
a completely different "skin effect" applies to the distribution of DC surface charges (within a Debye scattering length, I believe?).
*Also, mind that speed of light is a local property. It changes rather suddenly at and below the surface of a metal (indeed, which is an equivalent way to describe skin effect).
But this does explain when you should expect the current density to vary: if we use a semiconductor instead, its intrinsic (or lightly doped, as the case may be) carrier concentration is very small, and we can indeed saturate its capacity without much trouble (i.e., it doesn't melt or anything, indeed for low enough concentration, it needn't perceptibly warm up at all). Yet if we apply an electric field to the surface, that will attract even such meager charge carriers as are present (and repel their opposites, electrons/holes), so as to try to maintain charge neutrality -- the electric force is a very strong one -- and this can happen to such an extent that charge density increases markedly. Congratulations, you've invented a field-effect transistor.

Another critical aspect: notice the fields are crossed, E perpendicular to J.
So, this is also to say: metals simply don't transist. Which seems obvious enough I guess, but it took quite a bit of condensed-matter physics to finally prove what's going on; from a historical perspective say the early 20th century, this wasn't obvious at all. Heck, the notion of the electron itself was still very new back then.
(Mind, not to imply your state of knowledge is dated or anything; just as an indicator of what level of progress these facts are built upon.)
Cheers!
Tim