Please consider this edit to "Don't heavier objects actually fall faster because they exert their own gravity?". (Compare versions 21 and 23).
Motivation for these (last two) edits: I realized that my explanation in the question was incomplete, and that when I talked about the acceleration being dependent on both objects, I was actually using an equation of the force to prove it. Since in acceleration, force is divided by mass, it seemed necessary to explain why the closing acceleration of the two objects still depended on both masses.
I'm asking this question since I'm not a super experienced user on Physics.SE and would appreciate any help to improve my formulas or reasoning.