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Back to the Egg trays. They're plastic, slightly flexible but not flimsy - made to be reused many times but, apparently the delivery people haven't replied to requests to collect them. Their loss, my gain.
Each tray holds 36 "eggs" and each egg hole is open on all sides with a small hole in the bottom too. It reminded me of an "airpot" - those expensive pots with holes all round, the idea being that the roots grow out of the holes but shrivel up in the air. I've never been wealthy enough to afford one to see if it works.,
Now I'm not pretending these egg trays are airpots but, if I plant a seed/cutting in each egghole, I'll be able to see what the root formation is like before moving the seedling on.
The plan is to line the holes with newspaper, fill with compost, sow a seed or put a cutting in each hole and see what happens. They should be easy to remove once the roots start growing through the newspaper. If it all fails, I'm sure I can find another use for them -but it won't be chitting potatoes or storing eggs.

Even if you were wealthy enough for air pots , don’t bother. I got a 3lt one just to see what all the fuss was about. They were very popular amongst chilli growers for a while. I hate them. Keeping them watered is a nightmare.

You could strap them up into a square big 'airpot' if you found summat for the base.

Just use one as the base as well, air pots base looks like your average compost sieve. Horrible things. 

I’d stick to your idea of cuttings or chitting for you egg trays.