Fulminato Sabitha Armies + LoB Branch -> Chest: crimson sword + Scene Mestan Bomber (Dari)
That you get the Mestan Bomber Scene in addition to the chest is a leftover from 57.0 when the chest used the wrong switch. I mentioned it on Patreon and it will likely be fixed in future versions.
For optimizing this part we'll have to guess what to optimize for. Currently I'm assuming that the VP, LoB, Fuzkao and Nyst variables are representative for this one battle and will not matter much after this. So for the most part I'm just considering the checks in the Finale as targets I want to hit. I also don't see the assignments of targets to Esthera or Sabitha mattering beyond this battle.
Things that in my opinion are probably relevant in the future:
- killing Fuzkao
- sparing Lamia
- hitting 100 Mestan for Lilith RP
VP points might matter because they can change after the last check. Nyst score might matter because Nyst isn't dead yet. LoB truce might matter if we need to work with his troops again?
Beyond that the main difference between paths is the equipment you can obtain, and I think LoB branch is easily the best for that.
To be honest I am slightly tempted to go for the status immunity robe on the -Path. It means I wouldn't be able to spare the Lamia. But sending Esthera to attack (for the Holy Crest), Sabitha to Armies (for the Orc weapon) and Mestan to the island (for the Vibrator) I get a lot of cool equipment. I'm still able to kill Fuzkao despite him being unchecked (with Mage guild + New Givini 60, no investigation necessary unless you want to focus on the barrier at the -Path end.) This also gets Mestan to 100, 20+ Victory points and can get Nyst down to 7. If the Lamia aren't important this could be a solid plan.
Taking the +Path in order to spare the Lamia, I'd instantly switch Esthera to cover Fuzkao. That loses the Holy Crest, but gains the Ancient Crusader Sword, which seems better. That change gives some additional VP and Fuzkao damage, so here I can afford to not invest in the mage guild and still kill Fuzkao with the help of 2nd gathering investigation or by not choosing Mithyn RP at the +Path door. Of course investing still gives extra victory points. This is probably the plan I would choose at the moment.
I haven't looked at Fleet or Mythin Branch in detail yet, but I don't think they can get Nyst significantly lower, or any cool items. So I don't really see why I would go for them. I'll probably have a look at them later, so I know all my options, but I don't expect them to beat out the LoB branch.
Thinking about it, Sabitha RP could turn out be more important than an orc weapon. If that is the case switching the target to Mithyn would force the Bomber Scene to collect the RP, along with some extra VP that probably won't matter.