I was doing some research and came across this young man who does an excellent job of providing things to practise (and practise and practise) in order to learn to relax the voice.
It is a little geeky, but if one were to try his ideas for a few weeks, I am sure your would be amazed at the effect. Unfortunately there are annoying ads. The main part of the lesson starts about 3:00.
If you try it for 10 days, let me know.