We made drag-and-drop interfaces accessible by allowing users to TAB through the original list, press ENTER on the item they want to move, then use the arrow keys to move the item and press ENTER again when done (or ESC to cancel). After each move, the item's current position, and any necessary local context, was announced via `aria-live` region.

There are other ways that this can be accomplished with even fewer keystrokes, so I can't imagine a scenario where drag-and-drop interfaces would have to be avoided because they couldn't be made meaningfully accessible.