Oops, screen options TAB, not TABLE. Sigh.
If you switch the screen options table to 2 and then back to 1 the Update button will both show (2 col) and stay (1 col). Had to do that in a couple of places.
I didn’t check the name of the area where I got the widgets but it is as you say, Inactive Widgets, rather than as I said, Saved Widgets.
I moved a bunch of Inactive Widgets to the two sidebars I have on my theme and they showed up just fine until I switched to the Default theme and switched back to mine. Then there were NO widgets on my sidebars. Why is that???