Have you thought about sheetmulching? When we started TerraGnoma Community Demonstration Garden (
https://www.facebook.com/TerraGnoma), it was covered 6'-0" in Himalayan Blackberry bushes, non-native grasses, Morning Glory and Nasurtiums. As much as we wanted the edibles to stay, we needed a place to grow and build. We used large refrigerator cardboard boxes found free behind the local major appliance store at the mall, layered them and added 8-12" of arbor mulch, also obtained for free from a local arborist, a blend of oak, redwood and other local hardwoods. This was in November and by January, we were planting. Everything grew three times faster that first year, much like the plants in your hugelkulture beds prolly did I imagine. Planted pollinator plants specifically since we wanted to invite them to this space (Lavender, Citrus, Plums, along with many CA native plants: Salvias, Chasteberry Bush, Irises, Coyote Mint, Poppies, etc). The results in eight years have been astounding! The soil is rich with biota, and keeping our planting areas clear of the stuff we didn't want was easy. The Blackberry and original edibles were trained to stay in various areas and the grasses, including Crab AND Kukuyu were completely eliminated after a couple of years. Good luck, you're on the right track!
Roxanne, aka Ecocentrix