Thus, I have opted for making another couple of boxes for this purpose out of print paper boxes (that I get for free from my wife's workplace) and rigid cardboard, of which I have an abundance.
Over the last week, I have finished the first insert, and below you can see how it is going to work when placed in a box.
The plan is to make two such boxes, and then, after sorting paints into them, see if I need to make yet another one (which will then have to wait until after Christmas Eve).
This is a very time-consuming solution, but otherwise completely free - and free is always good for the hobbyist!
I hope to finish the second insert over the next couple of days, and then it is time to cut down and glue the boxes...