Here’s a slightly different variation (not quite the same, but similar) which only uses the Geometry tools and no Node Tool.
The history is saved with the AFDESIGN file.
Hi Aechidna,
1/ Select the two lower shapes (the lowest in the layers) marked 1 and 2 in white.
2/ Copy these two shapes and paste them at the top of the layers.
3/ Select the two shapes you just pasted and make a compound (Boolean operation "Substract" by holding down the "Alt" key on the keyboard).
4/ As the shapes are thick, convert into curves the ones that overlap the others: in my example the orange shape and modify them with the "Node" tool.