It occurs to me that if you didn't take branches to a wood recycler, then you wouldn't need a truck and would possibly have avoided the issue with the battery and whatever those costs will be.
Sawdust from cutting and small wood chips from chopping can be strewn throughout your property, and branches decompose quickly, probably within the growing season or two. One benefit from this is the promotion of growth of edible mushrooms. They love rotting wood chips and branches.
Are you required by law to take trimmings and branches to a wood recycler?