Hi Barbabra,
Hope all is well.
The best answer I have for you as a young gardener is to coppice them. This will stunt the root growth too.
I was so glad to find your question clearly stating you have vegetables growing in your hugel made of chinaberry wood. Everything I've researched says the wood is too allelopathic for a veggie garden. We live in the Kalahari desert in South Africa. We have this wood in abundance as most all farmers see them as too messy to keep long term and cut them off once a year.
I would like to ask however if you have experienced any allelopathy (stunted, not fruiting or seedlings not germinating) in this chinaberry bed.
Happy Gardening,
Waldo & Tilani