To have any useful reaction time, you'd have to keep that howitzer loaded and pointed roughly in the direction the anticipated missile would be coming from. The 155mm is a separate-loading weapon system, which means the round needs to be fully rammed into the chamber, propellant charge placed, and primer in the chamber before it can be fired. They are also heavy and immobile: even the M109 has a relatively slow rate of traverse if the tube isn't already pointed where it should be to engage the oncoming missile.
Railguns are nifty, but have they solved the difficulties in firing projectiles with an electronic payload? While I was in weapons development, the acceleration loads and massive EMP would melt/crush anything loaded into it - and since whatever is fired must maneuver to engage a maneuvering missile, it's important.
As an aside, while I commanded an artillery battalion in 1993, we were picked to test fire new 155 projectiles at China Lake, great experience for my young Marines.
Naval guns are not hand loaded. Since 155 mm is about 6 in and naval guns are 5” do you envision an issue adapting for naval use?
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.