Let's look at ways to make our tabledrag.js accessibility better. Currently tabledrag doesn't really work for screen readers, and we kept the fallback method with row weights. But tabledrag hasn't changed much since it was introduced in D7.
It's worth looking at ways to modernize this, so screen reader users can have a more equivalent experience. A number of more modern approaches to accessible drag and drop are in #2920006: Research accessibility of drag-and-drop grid interfaces..
In particular, ARIA is now much more broadly implemented by browsers, so things like aria-posinset may be viable to use now.