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Obviously different units (or to be perhaps more pedantic different metrics) will give different numerical values for light’s speed. However, I believe the relevant question is: Why isn’t the speed of light (as observed by an observer) in space twice (or 10 times) faster – or slower – than the value currently measured (using any metric you care to specify)? Any answer is independent of the units discussion.
The basic assumption In special relativity is that light always moves away/towards you at the speed of light. Assuming (even theoretically) that you are “riding on the photon” invalidates that assumption. If you invalidate the assumption you also invalidate any further calculations or conclusions or more accurately any conclusion you draw does not draw into doubt any special relativity conclusion since you have invalidated one of SR’s basic assumptions.
The basic assumption In special relativity is that light always moves away/towards you at the speed of light. Assuming (even theoretically) that you are “riding along [with] the beam of light” invalidates that assumption. If you invalidate the assumption you also invalidate any further calculations and conclusions.
Logical error here. Logic says that if A implies B it does not necessarily follow that Not A implies Not B. If when you don’t feel a force you continue to move at a constant velocity in a fixed direction you are in an inertial reference frame. It does not necessarily follow that if you do feel a force you are not in an inertial reference frame.
In this discussion, the reference frame is what is inertial not you. Inertial in this context means that the reference frame is moving at a fixed speed in a fixed direction with respect to (all) other inertial reference frames. If you are moving at a constant speed and direction with respect to to some inertial reference frame R then you are moving at some constant speed and direction with respect to any other inertial reference frame, in particular the inertial reference frame R’ which is moving with the same constant speed and direction with respect to R. In R’ you are stationary. No reference frame has primacy so you can take any reference frame to define your “true” speed including the reference frame where you are stationary.
Note that you can take either inertial reference frames or acceleration as the basic concept and define one in terms of the other: (1) an inertial reference frame is one which is not accelerating, or (2) acceleration is what happens when a reference frame changes direction and/or speed,
You are quite correct in inferring that the movement of inertial reference frames is a relative concept. Movement is defined relative to that of other reference frames.