Unless the people of discord and on this forum figure out some hidden mystery, it looks like the tribunal does indeed boil down to damage reduction. It seems that at best you 3 innocent people will die (the hardie boy that the female merc shoots, plus Theo and Angus when they charge in.) On top of this you can get Shanky, Elizabeth, Titus, Ruby, and Kim killed (well the latter is merely wounded in the hospital but who knows.) Ruby isn't really a part of the tribunal but I'm rolling her in there because she is yet another preventable innocent death.
Many of the things you did up to that point helps you pass a few checks before the confrontation, which distracts the mercenaries and thus makes the check to actually shoot them easier. If you are a really good shot, you might be tempted to just open fire immediately, but that gets Shanky killed because if you try to draw out the conversation he gets time to get away. On the other hand, if you try to draw out the conversation and fail, Elizabeth will get shot down. If you don't even have a gun in the confrontation, or if you just stand by and let it happen, shit goes to shit and Titus gets killed.
Apparently you might even be able to use a medicinal spirit as a molotov cocktail if you lack a gun, plus there two ways to prevent getting gunned down by the first shot: one is having the cuirass on, and the second having the sword equipped.
Finally, you can try to save Kim, and the check is made easier/harder by your relationship with him.
Yeah, all roads to the tribunal and there isn't a lot of variation besides saving a few lives - you can't talk the mercs into standing down, and you can't save everyone - and this I found initially disappointing, but the more I think about it, the more I find this appropriate. You've got 3 drunken mercenaries with PTSD, one of whom is clearly and vocally insane - people are going to die and the best you can do is minimize the casualties. When you consider that every single death here is that of an innocent whose only fault was trying to make things right for someone else, it gets pretty fucking tragic, and saving even 1 person seems like an achievement (besides Ruby, who was really into some shit, but if anything her suicide stings because its directly caused by you and is also completely preventable.)
At this point I am more concerned how much reactivity there is at the very end. I hope that if you did a truly shit job you can find the Deserter but fail to concretely identify him as the killer, and if you don't take photo of the phasmid the Precinct will refuse to take you back. My worry is that the phasmid is there as a get out of jail free card so that every build, no matter how disastrous, can get a cool ending where they ride back to Precinct 41 with the homies, but I sincerely hope thats not the case.