History of interpretation of Newton's first law

I did not do more than read Newton, and a few commentators, so my insight on this is probably meager. But I am sure that you are right that the inertial frame interpretation of the first law is only a modern ex-post-facto justification for making it separate from the second law. Newton certainly never used the first law to define an inertial frame, he just assumed you had one in mind, since inertial frames were not the focus of his investigation.

I think that the statements of the laws of motion are unfortunately following Aristotle more than Euclid. Since physics is no longer regarded as philosophy, we value independence of axioms over clarity of philosophical expounding, and this makes the first law redundant. But if you are stating a philosophical position--- that things maintain their state of motion unless acted upon--- Newton's first law is a neat summary of the foundation of the world-system.

Note that Newton does not state it as "a body in linear motion continues moving linearly". He includes rotational motion too, even though this is a different idea. I think he conflates the two to fix in mind the philosophical position that uniform motion is the natural state of all objects. In Aristotle, the natural state of massive stuff like "earth" is to be down at the center of universe, and of light stuff like "fire" to be up in the heavens, leading to gravity and levity. Newton is replacing this notion with a different notion of natural state. Then the second law talks about deviations from the natural state, and is a separate philosophical idea (although not a separate axiom in the mathematical sense).

The influence of Aristotle has (thankfully) declined through the centuries, making Newtons laws a little anachronistic. I think that we don't have to be so slavish to Newton nowadays.

Newton was aware of the importance of linear momentum and angular momentum conservation. One other way of understanding and his first law can be thought of as making the conservation laws primary. This point of view is both closer to Newton's thinking (it is what makes his "natural states" natural), and it is also a better fit with modern understanding. So it might be nice to restate the first law as "linear momentum and angular momentum are conserved".

All this is based on personal speculation, not on sound historical research, so take with a grain of salt.

I will argue that A,B, and C, are all wrong on the grounds of logic (and remark on pedagogy).

Firstly, A is wrong because the first law does not follow from the second law. The first law makes the specific testable predictions that in the absence of a net force, that the motion not change. But the second law makes no such claim because it is possible (see Nonuniqueness in the solutions of Newton’s equation of motion by Abhishek Dhar Am. J. Phys. 61, 58 (1993); http://dx.doi.org/10.1119/1.17411 ) to have solutions to $F=ma$ that violate Newton's first law. So it is not redundant.

As for B, I don't see a logical defect with Newton's laws, he posits an isomorphism between solutions to second order differential equations and spatio-temporal observations. Since he explains how to calculate these solutions, it's a method for making predictions that can be tested. And the first law simply decreases the allowed solutions to only contain those that also satisfy the non-redundant first law, as above.

As for C, if you read the first law as quoted by you very closely you'll notice he mentions forces, plural forces. So he isn't merely restricting himself to nonexistant perfectly isolated bodies. He's talking about special cases where the forces in play produce no net force. He's saying that if you had a very hard very level very smooth surface (so eliminating a net force from gravity and the surface) and then you keep dust from building up or winds from blowing at your device then it will slide or spin at a uniform rate. Sure, testing it would never be perfect, so if it was just a first law that would be a problem, but the second law allows us to bound how big the deviations are by the deviations from zero net force. But that then requires a separate theory of force, specifically force laws that postulate particular forces. This is implicit in the first two laws.

The third law is totally different because it actually constrains what kinds of force laws to consider.

So, the third law constrains what force laws you consider. The second law turns these force laws into predictions about motion, thus allowing the force laws to be tested, not just eliminated for violating conservation of momentum. The first law then excludes certain solutions that the second law allowed.

There is a place for all three laws, and they all mean something. Maybe we should teach them in the reverse order, but ... and this is the only point where I'll bring up any history: I assume the order given by Newton can be blamed on Newton.

Henri Poincaré (1854-1912) and Pierre Duhem (1861-1916) maintained that the law of inertia as formulated by Newton is merely a postulate.

Poincaré wrote in La science et l'hypothese (pp. 112-19), addressing how one would even know that a body without any forces imparted keeps moving indefinitely:

No one has ever experimented on a body screened from the influence of every force, or, if he has, how could he know that the body was thus screened?

Sir Arthur Eddington argued that the the law of inertia as formulated by Newton is circular, thus it conflates inertia to preserve motion with inertia to remain at rest. In his The Nature of the Physical World, Eddington gives a harsh criticism of Newton's First Law (my emphases):

Unfortunately in that case [of external forces acting on it] its motion is not uniform and rectilinear [as it would be if the 1st Law applied]; the stone describes a parabola. If you raised that objection you would be told that the projectile was compelled to change its state of uniform motion by an invisible force called gravitation. How do we know that this invisible force exists? Why! Because if the force did not exist the projectile would move uniformly in a straight line. The teacher is not playing fair. He is determined to have his uniform motion in a straight line, and if we point out to him bodies which do not follow his rule he blandly invents a new force to account for the deviation. We can improve on his enunciation of the First Law of Motion. What he really meant was—"Every body continues in its state of rest or uniform motion in a straight line, except insofar as it doesn't." … The suggestion that the body really wanted to go straight but some mysterious agent made it go crooked is picturesque but unscientific.