In most cases the allelopathic chemicals in plants will be broken down by natural processes within a year. When googling the California pepper tree I came across gardening articles particularly recommending it as a good
compost ingredient. I suspect they wouldn't have a long enough chemical effect to kill the grass. If you can pile them deep enough they would still work well in a sheet mulch. Most trees with allelopathic reputations are actually killing competitors through this mechanical process.
I've had good results converting lawn into garden beds by sheet mulching with thick layers of wood chips (think 12 inches or more) and then hand pulling the few bits that managed to grow up through that. Grass growing through that much mulch is very easy to pull. It's not an instant process, but it works well. If you have tree trimmers working in your area (or landscapers who trim trees) you can try approaching them to see if they would like a free dump site. If you are willing to accept a whole truck load, they are often happy to avoid a trip to the dump and the associated fees. Landscape trees are less likely than most other plants to be sprayed with noxious chemicals.