Originally Posted by
UNITED959
Give the tea plenty of time to brew so you get some of the flavor...

No, no, no, no!
As we've ascertained that the cocktail needs
real green tea,
don't brew it for longer than 60 seconds (40 seconds is usually enough). If you want the tea to be extra strong, then put more tea leaves in. And make sure the water isn't
too hot.
Overbrewing and using water over 80C will turn your fresh green tea into a bitter potion.
A 'how to make green tea guide' here;
http://www.ippodo-tea.co.jp/en/tea/sencha_01.html ( I highlight: pour the boiled water into TWO empty cups before pouring onto the tea)
(I'm still taking medication at the moment so can't test out the cocktail for myself)