I just went into edit mode, went into face select, moved one of the side faces up, and renamed the mesh to “Periscope”.
Then, I went into Bottom Ortho (Numpad 7 + Numpad 9 + Numpad 5), put the cursor on the lowest edge, then I opened the Shift-Ctrl-Alt-C menu and said “Origin to 3D Cursor” (which i discovered via experimentation), and went into the properties menu and set the location to 0,0,0. “gg ez”. Didn’t even touch the duplicate or join buttons.