“the space between Alpha Centauri and Earth is not actually changing, as anyone who measures it from either Earth or Alpha Centauri, or any other point in the universe can confirm. Only YOUR measurement is changing.”
This entirely misses a central point of special relativity: there is no such thing as THE distance between A and B. Any measurement in an inertial frame of reference is as valid as any other.
“Any measurement in an inertial frame of reference is as valid as any other.”
Of course, when you are doing the math. Yet, when it comes to reality, it’s still quite obvious that not all reference frames will represent an accurate picture of objective reality. For example, if you were moving at the speed of light towards Alpha Centuari, the distance between the sun and AC shrinks to ZERO, from your perspective, but still, the two stars would not collide with catastrophic consequences. So while your reference frame would be completely valid mathematically, it is NOT as valid a representation of reality as just about any other reference frame you could pick.