Is there something I can do so that, when dropping an item into a character's inventory, they are placed top-down instead of left-right? I.e., the same way as is done in MM7 and MM8.

I don't know of any way to do this.

I remember seeing something about it somewhere, but my memory is failing me on that point. I only thought to ask now because I'm in the middle of a game and find it annoying.

Install the newest GrayFace patch, it has that sorting by default.
https://grayface.github.io/

Thanks. Will give it a try.