There is no such thing as an ‘undergrown’ laurel! As a former landscape professional, I would recommend removal. Even with constant maintenance (shearing at least twice a year) the hedge will continue to get bigger and uglier each year. The interior of the hedge will not grow foliage, so the more you cut it back, the worse it looks. It is now listed as an invasive species.
As there is no way to harm this monster, go the cheapest route you can. Anyone with a ladder, a hedge trimmer, and an eye for a straight line can do it. Don’t waste your money.
