Rearranging widgets sans drag-and-drop

I’m trying to add widgets to my sidebar. I’m blind, and unfortunately can’t seem to find a way to reorder widgets without drag-and-drop which is inaccessible. I even poked around in the database tables, but if there’s some value indicating widget ordering then it isn’t obvious to me.

Is there any way to accomplish this without drag-and-drop? Failing that, what can I change in my database tables to move my widgets?

An easy fix for this, I think, would be a position field in each widget’s metadata, alongside its title. Represent it with a popup listing numbers from 0-n where n represents the current number of widgets. Changing this value and updating could then dynamically update the widget’s position in the list, thus simulating DnD completely from the keyboard.

Thanks a bunch.