As I understand it, the mod for 009 comes down to removing the white ring?
Yes. If you do it patiently, basically you can cut through the adhesive, making the mod reversible since the white ring will stick back.
Then I'll just remove it on the old pair and leave the new one intact for the future?
Or vice versa, remove it on the new one and compare it with the old intact one?
Whichever way. It also works with a single pad with or without it.
Or am I missing something, and the mod is not limited to just removing the dense white part from the ear pads?
It basically is. But keep in mind that I did not recommend this mod for the 009 in particular: it does change the sound, but one might prefer it the original way. With other headphones though, all of them sounded better with the white ring removed.
Note that the mod will make the pads more shallow - with my ear and head geometry it was still comfortable, but many people actually wanted to make the pads thicker, not thinner. In that case, I recommended removing the white rings and adding crescent shaped foam arc instead. Wool felt pads can also be used, but you will hear a lot of difference based on density, thickness, etc.