Here's why that doesn't work to explain aberration in a geocentric system in classical physics. Aberration changes in a cycle. In a geocentric system you have to attribute the motion to the star.
Imagine you have a real mechanical model of earth, sun, and stars. You hold the sun between two fingers, and all other objects move. On the earth there is glued a micro camera recording a video. Examining the video, you will find aberration, as seen from earth.
Then you take the earth between two fingers. This time, the earth is fixed and all other objects move. The camera records a second video.
Since it is one and the same model in both cases, all relative motion is identical in both cases. The two videos will be identical (disregarding the background). All movements of the sun and of the stars as seen from earth will appear identical in both videos.
Examining the second video, the geocentric video, you will find the exact same aberration, as seen from earth.
Aberration is not due to the motion of the observer with respect to the sun, but due to the motion of the observer with respect to the observed star. More exactly: due to the relative motion between observer and observed star. Thus, it doesn't matter whether the sun or the earth is fixed. You could even hold any star or planet between two fingers, and the video will again show the same movements as seen from earth.
The difference between the heliocentric and the geocentric view is: The heliocentrist says: aberration is apparent, it is an effect due to a movement of the observer. The geocentrist says: aberration is a real additional movement of the stars while the observer is not moved.
So indeed, like you say, in the geocentric view the motion is attributed to the star.
Note that the additional movement of the stars does not imply any problem with gravitational forces for any model implementing Mach's principle.