Worming was my first thought too. Were they wormed when they arrived? Were they daggy when they arrived? What breed are they?
We use normal hand daggers, not shears and not electric or battery powered daggers. It's not the most pleasant of jobs, but your confidence and speed do improve. With hand daggers, you're not usually cutting through the dags but through the wool between the poop and the skin. If they're very tight, use the scissors on your Swiss Army knife, but don't try to pull the dag away from the skin to get your daggers underneath as that's a sure way to cut the sheep. It looks scary and you take your time - no rush, you don't have 3,000 to do. Make sure you protect a ewe's vulva and tail as you dag, and sit her on her behind for part of the procedure to be sure you get to any underneath bits while being able to see clearly. If they are standing, it's a great help to have someone else holding the front end.
At certain times of year you can peel off dry dags, mainly coming up to shearing.
If your ewes are a big fluffy type, and particularly prone to mucky back ends, then a big clearance up both back legs as your farmer neighbour recommends will be effective and help you spot signs of fly strike.