
This is a situation that really has no answer other then to move your raised beds.
The root system of the Gum Trees will infiltrate even wire mesh if placed in the bottoms of the raised beds.
Growing in containers might be a good option for you.
Here are some links with more information.
https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/eucalyptus-tree-root-damage.htm
https://www.gardeningknowhow.com/edible/vegetables/vgen/quick-guide-to-container-vegetable-gardening.htm
https://www.gardeningknowhow.com/special/containers/designing-your-container-vegetable-garden.htm
https://www.gardeningknowhow.com/edible/herbs/hgen/growing-herbs-in-containers.htm