Leave the Christmas berry mulch or remove it?

Mulching it and concentrating the wood chips in the area you will be growing in is what I recommend. Even though it has toxic sap, that will quickly be broken down by microbes and will not inhibit the effectiveness of it as a mulch. You want to be careful not to scrape up too much of the thin soil you have, so adding a thick layer of mulch will help build more soil where you need it. Also be careful of erosion after clearing, and the subsequent weeds/grasses that will thrive when the land has been cleared.

I also recommend going slow and steady, and instead of clearing the land and getting rid of all the trees, doing it slowly, clearing only what is necessary at the time, and planting in between your existing cover, and as those trees grow, clearing out the christmas berry. This is a huge carbon store for you, and if it is all dropped at one time, it will quickly (within a year) be gone and then you will have to grow other things or import mulch to keep up the fertility of the area.

Also, think of the christmas berry as a resource, as I mentioned today in the Office Hour, Richard Perea used to use the christmas berry very effectively when he was living out in the Kau region.