I agree with Julie about the overfilling, a problem you already suspected. You would have had almost enough batter to make two more layers, another 4” and another 5” in diameter, filling all pans to the halfway point as Rose recommends. That is, to a depth of 1” in your 2” high pans.
However, I believe that you’re also experiencing classic signs of too much baking powder as Rose describes in her Understanding Butter Cakes section in TCB: “Too little baking powder results in a tough cake with a humped top, compact crumb and poor volume. Too much baking powder results in a coarse, open, fragile crumb and often a fallen center.”
This may have come about through the switch to smaller 2” high pans or improper measurement or a combination of the two. In any case, there are some pretty simple fixes along with careful measuring.
But first, it would be helpful to know what size pans you generally would prefer to use at the 2” height. If you’d like to move directly from 9” to 9” but only change the height, you can leave the baking powder as is and multiply the ingredients in that recipe (p 39 TCB) x 1.33. But for smaller pans, you’ll need an adjustment for the bp. Let us know.