I concur with you (that this is an excellent introduction)!
Imo, your suggestions are more for intermediate/advanced active listeners that need to interact with folks in their job (e.g. bartenders, reporters, middle managers...).
Still, I feel being repetitive (e.g. 'It sounds like XYZ...is that right?') is better than nothing. Sometimes, training wheels aren't bad when learning how to ride a bike.
author here. Exactly, “it sounds like” etc are training wheels. Use them while you figure out how to do the technique. And yes, when you’re learning, it can sound stilted. As you master it, you don’t need to use those exact phrases any more.