I am a Team Leader for a company,on a major contract and I run the Call Entry Team. We have a handle target of 3 mins, but I never enforce this, if the job is getting done then let it go.
The Agents have targets of web refferals and call logging, which they normally can hit no probs. Agents are not measured individualy on customer satisfaction, although my old Team, notebooks was, the Entry Team is none technical..ish.
Your TL must be under some pressure to reduce AWT, (average wait time) on his Team to achieve a Service Level. Still it's not good management to me, as it sounds like all this has had a major effect on your morale.
Ask for a one on one, and explain how you feel.