In the “Move Item” dialog I think you should give checked items less priority (lower on the list) or even better add a toggle whether checked items should appear. I often have a lot of checked items appear before the item I am searching for. This is also relevant for the “Item Finder”.
Thinking of it, the defaults of showing completed items in the “Move Item” and “Item Finder” and hiding them in “Search (in doc and global)” is opposite to what is most useful to me. I use “Move Item” and “Item Finder” for all the stuff I use often (they are obviously unchecked), whereas I use “Search” to find something uncommon. From my perspective I would guess most use it that way