Plants usually don't rotten apples, or grease, it's the microbes/decomposter that break them down and help the plants that follow after.
There are fungi that break plastic and oil spill so a bit of grease,
should be fine. I know that koji, will also digest oil too. And microbes in septic tank also digest grease. I think that as long as some woodchip is added to the mix, microbes will remove it in no time.
Also it turns out that in return for minerals from the soil, tree trade fatty acids in addition to sugars with fungi.
https://phys.org/news/2017-06-biology-uncovers-high-fat-diet-fungal.html
Iterations are fine, we don't have to be perfect
My 2nd Location:Florida HardinessZone:10 AHS:10 GDD:8500 Rainfall:2in/mth winter, 8in/mth summer, Soil:Sand pH8 Flat