I'm not trying to give you a hard time, but it sounds as if you're looking for an answer to reinforce a decision you already made? If not mea Culpa.
You asked... "What is the minimum barrel length I can get away with"
It sounds to me like you want more than a match / Steel / range gun? Maybe for carry also?
That said, IMO for steel longer is better. I think an all steel gun with a longer sight radius goes hand in hand with more weight for quick follow up shots.
Some say too much weight makes for an over swing on horizontally placed plates, I never felt this.