Righto, while turning on my old shiposting laptop and grabbing my drawing tablet, it dawned on me there is a way to approach the pivot issue which lets you twist the stick out of the way while maintaining the strength of the mount on the table and making a more lockable moving part - by placing a hinge in the Boom arm rather than a pivot in the mount.
For a pivoting system, the clamp and mount will remain in the same position no matter where the stick is moved to, so if there is a hinge in the Boom arm you can still twist the stick out of the way just like a pivot and the mount stays in exactly the same place so there is no loss in that regard:
The above picture suggests there could be a drawback in the length of the boom arm is jutting out along the desk but if the mount point is further back the hinge point can be further back too and keep most of the arm under the table.
Further to the above, I have three thoughts on approaches to the hinge itself:
1) The Folding Bike: In my younger years I had a Giant Halfway folding bike. Wonderful thing, it's the heavy duty hinge and clamp on the frame I remember:
Screenshot taken from this video:
View: https://www.youtube.com/watch?v=kR-Bwrf2u2I
The heavy duty locking lever and hinge kept that frame solid as a rock when in use and was a simple unclip and the thing was folded in moments. Fast, efficient but very heavy duty. It would need a hinge and clip up to the task which might be costly to manurefacture... so...
2) Collar over the hinge: Another approach could be having a hinge which a metal collar slides over, stopping it from being able to move:
This however may allow excessive moment in the hinged section and the collar would need some kind of arresting system. It's viable, but then I had my final thought with takes the hindge out of the equation almost entirely while playing:
3) Boom boom shake the room: The boom could secure to the mount, only using the hinge when one wants to move the arm out of the way:
The hinge could be inside a slightly thicker boom arm, which secures to the mount with folding clips. Unclip the arm, and slide it out along the hinge pole, then simply fold out of the way. When you want to play again, fold back and push the boom arm back over the hinge. The hinge then only has to be strong enough to carry the weight of the stick in its stored position and doesn't have to be heavy duty enough for game play:
I prefer idea 3 as the hinge is removed from the game-play strength aspects of the design, the arm should be able to be clamped firmly in to place to the rest of the mount while playing.