Are you using water at a rolling boil? If I'm using a kettle, I pour the water into a glass measuring cup and then into my pot so it cools just a little bit. I also keep my zoji at 208 and try not to have the water hit directly on my dry leaves when I fill my pot or ingenuitea. It might be my imagination but I think it keeps bitterness down a bit.
As for the dry mouth feel, that's astringency. Some teas like Darjeeling have more astringency than a Nilgiri or an Assam. Some of the Nilgiris that I have are also totally smooth on the first steep and a little bit astringent on the second.
The beauty (and sometimes frustration!) of tea is that there are so many kinds, you can find what you like best, but there's always room for exploration!
