For me, it's kinda similar, only with the Brotherhood of Steel. My intent is to steer the Brotherhood back towards how Elder Lyons did things before, with the end-goal of ending up like the Midwest Brotherhood. Yeah, I know it'll splinter the faction again with the Outcasts, but if Maxson's Brotherhood really did have the interests of the Commonwealth first and foremost in their minds, they'd put the technology they gather to use in protecting the Commonwealth. To that end, I've made sure to install the Danse Dilemma mod, as it even has the option of telling Lance-Captain Kells not to bother the Railroad. Like the mod implies, it'd be hypocritical to destroy the Railroad after standing up for Danse, but even then the Railroad would likely not pick fights with a synth-friendly Brotherhood. If you're going without mods, then this would be the cutting-off point for the Brotherhood to side with the Minutemen.
When it comes to the Minutemen themselves, they'd remain as-is. My Brotherhood isn't out to rule over the Commonwealth, just protect it from abuses of technology. There's still the feral ghoul problem, and the raiding super-mutants to deal with, both of which caused by nukes and FEV respectively. The Institute naturally would have to go, as they care little for the Commonwealth and, in my opinion at least, are outright evil, kidnapping and experimenting on people and have straight-up caused the Commonwealth's super mutant problem. I would sound the evacuation at least, because there are certain lines you don't cross. Killing non-combatants is one of them. But when it comes to the day-to-day protection from raiders and most creatures, the Minutemen are the ones on the front-lines.
Essentially, the Brotherhood is the Superman in the Watchtower, while the Minutemen are the Green Arrow down on street-level.
When it comes to the Mechanist, her heart was in the right place. She truly did want to make life better for the Commonwealth's citizens, and the mask of the Mechanist helped give her the confidence to do it. Her mistake did cost people their lives, though. But an eye for an eye makes the whole world blind. Her sentence would be community service, helping to maintain a new robot network operated by the Brotherhood to patrol the busiest of trade routes between settlements. Some might argue that this isn't really a punishment at all, and I can certainly understand their stance. But I don't think she should be held responsible for the robobrains reinterpreting her orders.
For DiMA, he would stand trial. But I would do everything in my power to ensure that Acadia not suffer as a result of his actions. Yes, he is the leader of Acadia, but his actions were his own, and thus so is the sentence. Acadia and Far Harbor can still work together and benefit from one-another. But sadly, the Children of Atom would have to go. It's become clear through the encounters in the Commonwealth that they've become far too fanatical to be reasoned with to work together long-term, especially with the evidence of kidnappings in the Boston area. It's unfortunate, but necessary for the long-term safety of everyone.
Nuka World is pretty cut-and-dry, really. But it'd be the Minutemen saving the day on this occasion, moving in and restoring freedom to the area. It'd again become a trade hub for folks, with the Minutemen running security.
I know this probably reads as hopelessly idealistic as it gets, but I don't think that a post-apocalyptic wasteland means that government and civility is impossible. It'll be an uphill struggle for sure, but it can be attainable with cooperation between the factions. I know I left the Railroad out of this one, but they seem to me to be focussed entirely on freeing Synths, which is totally fine and something I'd encourage and assist with. Synths may not be human, but they are people. And under the protection of the Minutemen and the Brotherhood, people would have rights that they'd lay down their lives to protect.