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[MadMojoMonkey]

The law of inertia (Newton's First) states that, in an inertial reference frame, a body in motion will continue along its path in a straight line at constant velocity unless acted upon by another force. In the case of the earth/moon system, the "force" in question is earth's and moon's gravity. If gravity is a force acting upon the moon, causing it to change direction, it would be accelerating (undegoing a change in motion), and this would be reflected in a loss of change in relative velocity. It would slow down not move in a straight line, and start falling but accelerate towards earth. That is has not done it is doing so is evidence that the moon is not accelerating Newton's Law is an apt description... it is not undergoing a change in motion, its inertia is maintained in an inertial reference frame.

SMH

bold for emphasis
Newton's First Law is a definition of what is an inertial reference frame. It defines the context of the other 2 laws.

The moon is moving in a straight line at a constant velocity. If it were literally moving in an ellipse, then it would be slowing down, or would require a source of energy to stop it from doing so.

It's a straight line through curved spacetime in Einstein's model, but a curved line through flat spacetime in Newton's model.
The underlying mechanics behind the motion are different, but the descriptions which emerge are (to so many decimal places) identical in the context of Earth-Moon or Earth-Sun.

It is literally moving in an ellipse in an inertial reference frame in the Newtonian model. It is speeding up when it moves closer to the body it orbits and slowing down when it moves further away. Bodies in elliptical orbits do not move at constant speed. Conservation of energy states that when their separation increases, their gravitational potential energy increases, and their kinetic energy decreases. The opposite is also true. That's why when you drop something it accelerates (keeps getting faster) toward the ground. It is moving from a state of higher gravitational potential energy to lower, and it increases in kinetic energy as it does so.

Gravity is not a force that pulls things together. It's better to say that the presence of mass causes curvature of spacetime, and we see this curvature in the form of gravity. Things being "pulled togther" is just spacetime curved to the point where collision is inevitable.

You're somewhat confusing in writing off the Newtonian model altogether. While it is technically inferior, it is at least intuitive. In its inferiority, it still describes all of the solar system aside from some tiny perturbations in Mercury's orbit, so it is a quite useful approximation, too, while being MUCH less complicated in the math.