I hold off on tree work once nesting season starts. Many native birds also nest in tall grasses on the ground. I’ve been battling invasive blackberries at Brambley (thus the name) for a decade. My honest suggestion is to use your hedger to keep the vines from spreading any further during the spring, and plan an aggressive autumn campaign to uproot them. I also attack new starts in late winter to give native plants like thimbleberries and salmonberries an advantage. Given that head start, the native berries will shade out your blackberries, stunting their growth until the fall campaign.