Got the encounter with 4 escorts and immediately ran away. No special text, and the next time I encountered him with 2 escorts as if nothing had happened.
I'm pretty sure you have to do . . . something when he has 4 escorts to take advantage of his pride to get him to make a mistake so you can fight him alone. I'll try letting him beat me up next.
EDIT: I let him beat me up with 4 escorts—no special text, regular encounter with two escorts next time. I'm still thinking the key is somehow to jump into the water. That'll make him feel like I can't stand up to him, so he won't even bother to bring goons along next time.
As you make your way along the docks, you hear shouting and see the glare of flashlights following you. The officer from earlier fires off a few rounds, taking chunks out of nearby crates.
The whole posse catches up with you by the water's edge. It should be easy enough to ditch them by jumping into the water, but that'll just prove no one can stand up to them.
Note: Even if you the player know about getting Stone alone, from reading the wiki, you probably can't spade this until your character listens to the Vigilante Recording in game.
EDIT: Another idea, from way out in left field: maybe I can find The Vigilante's old mask (and/or army jacket?) in the Abandoned Subway. We know that's the last place he went before he disappeared. And a mask hides your face, so Stone won't know you're not really The Vigilante. Maybe that'd set off his pride. You know "So, you've come back for more, Vigilante? You pissants never learn, do you? I'm going to enjoy breaking you like I broke this gun here. Boys, take five. I'll handle this punk myself." I just hope I can find the (extremely hypothetical) Vigilante relic in the dumpster and don't have to solve the mystery of getting past the brick wall.