I had forgotten that there can be a single button on the search tool bar. I had the tweak set to show me the original interface that doesn't use the button.
That button and the action now show the same menu, both with hierarchical menus. This means that the "Manage" lines are now in the saved search action as well. The both use the dedicated saved search icons.
The keyboard shortcut code has been improved to try harder to position the saved searches menu under the toolbar or menu item for it. If it fails because no toolbar or menu is available (or usable) then it positions the menu in the upper left corner of the booklist, like this:
EDIT:
The keyboard shortcut for Saved Search doesn't work in current source. I hope to fix it today. Fixed.