It isn't as bad as it looks. A good pole saw ran by one person while another pulls the cut limbs back will open up the shrubs to a chain saw fairly fast. This is similar to the fence rows at my place in some areas, nothing worse than those dense shrubbery to cut unless it is dense shrubbery overgrown with saw briars. You will need at least one person pulling back the cut limbs so the person running the pole saw can just keep whacking them down.
You will be surprised how fast that you can open that tangle up to expose the trunks.
You may need to work from the side opposite the fence for easier access.
For that thick hedge, I would cut it to within ground level, it will grow back at a rate of about 4 feet a year which you will need to keep topped to prevent a nasty regrowth that will look like the original in 5 years. The only way to kill that is to dig out all the roots. I don't even think 2-4D will totally kill it.
Goats do love it though and that my be an option to use to thin out the ground level stuff prior to tackling it. I do hate goats though as they climb on everything, stick there heads through small holes in fences and get stuck. A real PIA.