GR also says that your gravity is indistinguishable from an acceleration. Do you not believe in GR?
GR doesn't say that, your selective portion of the equivalence principle says that.
Perhaps you can explain the Equivalence Principle to us then, since you are much smarter than Einstein?
A
local experiment cannot tell the difference between gravity and an accelerating reference frame.
That is what GR says. You forget the bolded word.
One non local experiment that GR says can tell the difference between gravity and an accelerating reference frame is dropping two balls in a vacuum, one above the other. GR says that in a gravitational field the distance between the two balls will increase over time, while in an accelerating reference frame the distance will stay the same.
Another experiment to tell the difference between a gravitational field and an accelerating reference frame that you can do on earth, measure the acceleration of a dropped object at ground level, and measure it at a significant height above sea level. In a gravitational field the acceleration will be different, in an accelerating reference frame it will be the same for both objects.
And being able to use these experiments to tell the difference between an accelerating reference frame and gravity, it doesn't go against the equivalence principle, because nether experiment is local.
If you don't know, a local experiment means that all objects in the experiment must stay within an infinitesimal distance of each other.
Also, if you believe general relativity is right, why are you trying to argue that gravity waves weren't found. If the FET agrees with GR, it must have an explanation for gravity waves.