It seems as if Gemini hinges vary a bit… (See
this topic.)
When I hold mine in that sort of position, I prop the screen open; it's hard to describe, but I put one or both middle fingers under the hinge, use forefinger(s) to hold the edge of the screen, and rest the corners of the keyboard on one or both palms. (That's how I tended to hold my Psion. Thumbtyping is reasonably comfortable. If needed, you can hold it in one hand and touch the screen with the other.)
Not ideal, but it mostly works!
I'd be surprised if it's possible to tighten the hinge after manufacture, but I too would be interested…