For those who are afraid to try embroidery on wood.

I've been experimenting some more today, so I took more pictures.
The box I had was 80mm square and the balsa strips were 75mm so a join was needed.
I hooped tearaway stabiliser and scribbled over it with a glue stick - particularly down the centre line where the join would be. I laid two pieces of wood on it, pushing them together firmly. (They are not exactly the same length so you can see where the join is.)
Next I embroidered the design. On this occasion I used wss on top (that was the experimental part.)
When the embroidery was complete I rinsed the satabiliser away under the tap and then put the wood to dry.
As my box has a hole in it, I glued a piece of balsa inside the lid to cover it. When the embroidered wood was dry, I covered it with PVA glue and laid it upside down on a cutting mat with a heavy weight on it.
Lastly I cut away the extra wood and lightly sanded the very edges to chamfer.
I don't think I will use wss again. The water has affected the fibres of the wood, making the surface look rough.