I like the idea of getting rid of the view screen. I think the sphere is a great idea.
I remember seeing the astrometrics lab and thinking "Wow, this is where the bridge should be" (the difference being that that lab was inside a sphere - I imagine yours would be an overhead preojection?).
Yes - it would occupy a column of space in front of the Helm station and emanate from there in three dimensions. (I love the astrometrics lab too; I always thought it would go nicely on the top of the primary hull, where the bridge usually is.)