I havent a solution I am afraid but I wouldn't bring your bike or dog this way because when the local farmers cut the hedgerows the lanes are chock full of needles and I just cut across their fields instead (except for one with English Longhorns filled with mums and calves).
PS You can buy tyre liner but I would ask around if they really help before you buy, here is an amazon one
Amazon.co.uk: tyre liner