The man moves slowly down the long glass corridor...
Then suddenly freezes, seeing --
A deer standing just/right on the other side of the glass, staring at him.
1) Could you think of a better alternative than on the other side of the glass here?
2) Is there any small difference between just and right in this particular context or are they complete interchangeable?
They are different. I'd use "just". "Right" fixes a position. "Just" emphasizes proximity.