Clearing invasive trees on hillside Kauai

I’m almost 3 months into clearing steep hillside of invasive trees .making check log terraces planted with vetiver along contour with sweet potatoes.I back filled terraces with decaying wood and leaves ,brown longon leaves and guinea grass leaves .im also planting fruit trees papayas ,soursop ,banana etc I’ve bought a small chipper that chips 3 inch branches.theres a huge supply of hau bush that chips real small also cutting banana stalks in half for water .my problem is how to get rid of umbrella tree and invasive gauge from growing back ?

Welcome to the forum!

From your descriptions it sounds to me that the best way to keep those trees from growing back would be to make hugelkultur beds on top of where the invasive trees were.

Hugelkultur beds are mounds of wood and covered with dirt.  This would smother those invasive trees.

In case you are not familiar with hugelkultur we have a whole forum devoted to that subject:

https://permies.com/f/117/hugelkultur

Not sure what you mean by "guage", but if it's any kind of tree or bush, maybe you can smother the stumps with something like old carpets, perhaps underlain with plastic (carpet keeps sun off of plastic so it doesn't break down as fast)?   Or maybe dig out around it a bit and then pile some chips, sticks etc. over top and burn?....might get along with making biochar which might be a good thing in your situation if you have lots of woody stuff and in high rain/poor soil situation....