Being an aviation sailor, I have no knowledge of artillary. However, if the system can be upgraded to fire the projectile at such velocity, can’t the loading process and positioning of the turret also be upgraded. Must the projectile be fed in the same sequence as you state above? I’m thinking some kind of super sized Phalanx without the high speed feed, but as maneuverable. Serious question and thanks for you service.
To modify this system to run at higher speeds - using a sliding block system, for instance, means making the system incapable of firing standard 155mm ammunition. There have been 155mm SP guns that have been automated to load and fire ammunition faster but they have required a heavier loading system to do it - like the French GCT gun system or the PzH 2000 or the US Army's Crusader - which makes the turret very large and heavy.
To make something large and heavy move faster requires very large actuation systems which in turn, require much greater power.
Very quickly you begin to see a 70 ton gun system which can't cross bridges and is very hard to transport by air or sea to the forward combat zones. It's all possible - but the penalties are weight, expense and an entirely new ammunition system.
Don't even consider the towed 155mm systems - dang things are heavy, manually operated, and slow; my best gun crews were flailing for 12 minutes to emplace and ready their guns to fire when they rolled into a new position. And that was with ten strong young men doing their level best!