Inoculate the mulch first. Allelopathic chemicals are broken down by fungi, so after you
feed all the branches into the chipper, pile the mulch up and throw any
mushrooms you can find onto it. Keep the pile well watered and in a few weeks, you
should be able to find hyphae (white threads) growing on the pieces as you dig into the pile. When you have some good fungal growth on the mulch, then you can spread it around and allelopathy should not be a problem. The fungi will continue to break down the mulch and build up your soil food web under the trees and in the garden.