^ Annual aberration is the ratio of Earth's orbital velocity (around 30 km/s) to the speed of light (about 300,000 km/s), which shifts the Sun's apparent position relative to the celestial sphere toward the west by about 1/10,000 radian. Light-time correction for the Moon is the distance it moves during the time it takes its light to reach Earth divided by the Earth-Moon distance, yielding an angle in radians by which its apparent position lags behind its computed geometric position. Light-time correction for the Sun is negligible because it is almost motionless during 8.3 minutes relative to the barycenter (center-of-mass) of the solar system.Notice that the moon does have light-time correction and apparent angular displacement -- because it does orbit the earth. The sun, on the other hand, does not orbit the earth, and as a matter of fact doesn't move all that much in 8.3 minutes, (no where near 2.1 degrees!)
Ok lets go back to our transit at dawn experiment. Only this time the earth is fixed and the sun is orbiting the earth. Now as the first light of the sun is seen at the horizon, point the transit at it. Then 8.3 minutes later measure the difference between the apparent edged of the sun and the horizon. You will see a difference of apx 2.1 degrees on the transit. I am assuming that with the sun orbiting the earth you will agree that its apparent position differs from its actual position by 2.1 degrees, right?
Now lets repeat the experiment with the Suns position fixed and the Earth spinning in place. Now as the first light of the sun is seen at the horizon, point the transit at it. Then 8.3 minutes later measure the difference between the apparent edged of the sun and the horizon. You will see a difference of apx 2.1 degrees on the transit. This is the identical experiment and the identical result except that instead of the sun orbiting the earth the earth is spinning. As far as our observations go the results are identical.
There is no difference between the Earth spinning in place or the sun orbiting the earth, the suns apparent position vs actual position is the same.