Thanks for the detailed feedback. The latest version now supports this workflow: tabs selected directly in Firefox's tab bar with Ctrl, Shift, or Command click can be moved from the new "Selected Tabs" menu item.

The selection-window workflow is still available as "Choose Tabs and Groups", so you can use either direct tab-bar selection or a custom selection window depending on the tab structure. If you previously customized the move targets, you may need to enable the new item from the settings page.