Any idea how to use EE Keeper to modify items that are not allowed to even be moved from an inventory space?

You mean to remove it from inventory? Select the character, select the item, then hit Clear Item. Or you can change it to some removable item then drop it in the game. Maximize the window or widen it in case you don't see the buttons.

I know how to remove and.change items.

The question is how to remove the unmovable property from the item.

^
I thought you might mean editing items, but wanted to get the most obvious answer out of the way. Because, you'll need more "advanced" editor for that purpose, such as NearInfinity or DLTCEP. Keeper is purely a save editor.

Drat, how tough is NearInfinity to use?

That does seem like the solution, so I will mark it as such, but I've never used it before.

Much, much more difficult than EE Keeper. Not to be used unless you know what you're doing.