I experienced the same pain my first year. There was a 2 acre park that was infested with clad (from 30 years of the Annual 4th of July picnic), I could not swing fast enough. It seemed that every 3 sweeps, I hit a target. I have learned to slow down a little after getting tennis elbow. I was pulling anywhere from $30 to $40 worth of clad each day in the beginning without using a pin pointer. I would start at 8 AM and swung until 4:30 PM, drive home, eat dinner, and then go back for 2 to 3 more hours.
The exercises look kind of goofy when done at the gym Exercises for Tennis Elbow: 5 Moves for Rehab but if you look at them, they are all designed to strengthen the muscles in your forearms. I hardly ever see people working these muscles at the gym. They are really small muscles compared to the others that most people concentrate on developing, but for us they are a major player in our hobby. Do these exercises 5 times a day and you will feel the benefits.
Patience Grass Hopper, no exercises necessary, just slow your roll... The pain is not worth it, slow down and enjoy the hobby. I understand the notion that there is so much Terra Firma an so little time, but this is to be an enjoyable endeavor and not a pain filled activity. You are simply swinging the coil too aggressively.