Manually Modify widget_nav_menu

I have several widgets on one WP installation that I want to quickly copy to another installation (exact database copy with URLs modified) and only change the Title of the blocks, I see that the footer widgets are in the widget_nav_menu option table row and have tried copying this value between installations however it appears that the value does not transfer for some reason. Is there another table row I need? It seems even if I copy it without changing anything the widgets just don’t stick.

What can I do to easily copy these widgets between installs?