If you dropped a 1kg hammer and 1kg of feathers the feathers would hit first.
That’s simply because the feathers have a much larger volume.
Not only that, the tidal forces on the feathers would be different to tidal forces on the hammer and produce an effect - not sure what, but it would be measurable - probably elongation of the feather bundle.
By tidal I mean resulting from the gravitational field gradients.
In the hammer and single feather case the tidal forces would again be relevant.
Are we measuring the distance to their center of mass, or to their lowest point?
Well no, the entire nature of the original argument is based in facetious pedantry so pointing out that the hammer and feather’s mass both have to be considered in the earth-hammer-feather system regardless of which is being dropped is an appropriate response.
I’ll go one step further and point out that the earth is gaining about 1kg per second from space debris, but losing just over 3kg per second in gases from the atmosphere (we’re imagining an evacuated chamber, not a lack of atmosphere, remember?). Since the gravitational effect of the atmosphere at sea level effectively cancels itself out, the 3kg lost per second can be ignored and the one that falls the fastest will be whichever one you drop first due to the 1kg per second gain. At a certain altitude above sea level this reverses, and whichever one you drop second will fall faster. If you want to find that magical altitude at which the loss and gain cancel each other out, you’re on your own, that’s too much pedantry for one day.
What illogical experiment set up are you positing where this is true? Start heigh measured by center of mass and fall time until perimeter hits ground?
If you work on centre of mass then there is a good probability the feather centre of mass will never hit the ground and almost absolute certainty the hammer centre of mass will not especially if it hist a hard surface.
If you adjust to account for volume of object - using the edges - then the release height of centre of mass will be different and so the acceleration.
Then if you take into account the different tidal forces on both objects there is absolutely no way to compare them.