(Possible book spoilers, will try not to reveal details.)
After reading The Masked Empire, I ended up deciding to reconcile Celene and Briala. To others who read the book, I know that it hardly seems at all healthy to reunite them considering what Celene did, but I don't doubt that Celene genuinely cares for Briala, and considering her circumstances and the nature of The Game, her actions were necessary for her to become Empress. I know that doesn't justify it, and I agree that it was terrible. But one shouldn't make moral judgments of another person's actions in absence of context, which in this case means Orlais, a country whose people and society hold cunning, deceit, intelligence, ruthlessness and ambition as the highest virtues of nobility and leadership. Celene was raised in a world where every one of her peers embraced the dictum "The strong do what they can, and the weak suffer what they must." And while I deplore her actions, I concede that they were necessary, and thus tolerable. Although Briala suffered enormously because of Celene's actions, the fact remains that they do genuinely love each other, and each truly wished to see the other's dreams and goals come true.
As for Gaspard, I find myself conflicted about how I feel about him, but ultimately consider him an inferior alternative to Celene. Sure he has a chevalier's honor, and he despises The Game as much as I and every other human being does. But he's also a militant nationalist who has no other plan than to expand Orlais' borders. Sure it's possible to arrange peace between Orlais and Ferelden, and thus direct his focus towards Tevinter, but even a war with Tevinter could have undesirable consequences if he can't keep the people of his empire to work with him. He would have been a poor Orlesian's Louis XIV; he would expand Orlais' borders certainly, but he has no diplomatic skill, and his hatred for and likely refusal to play The Game would undoubtedly enrage the nobles under him and subsequently compromise his ability to actually govern. His army would be the only thing keeping him on the throne, which is pointless if he has no bureaucracy and administration to work with him, which means nobles who tend to get unruly when someone ruins their Game. Add his prejudice towards elves, and you have a man who would shake up Orlesian society to the point of creating more instability and civil infighting in the long run.
Letting Briala rule through him is equally as bad, as her attempts to uplift the elves would likely result in a very rapid overturning of the status quo, and that means backlash. Her reforms would bring a lot of change to quickly and would become incredibly hard to enforce, especially when the puppet emperor can do nothing to temper the changes enough to assuage the conservatives of his empire.
As for forcing all three into a truce, I'm afraid that option does nothing in the long run that benefits Orlais. Celene's rule would be as tenuous and vulnerable as before, Gaspard would still be able to challenge Celene and her plans for Orlais, and Briala would end up with nothing and continue her shadow war to emancipate the elves. They may be three of the greatest minds in the empire, but their goals and beliefs are too disparate to ever allow them to cooperate for the greater good of Orlais.
Thus, Celene and Briala are left. This option is truly the best option for both Orlais and Thedas. Briala would still be able to get reforms passed to improve the lives of the elves, but she'd also have Celene with her to execute the changes with enough tact and precision to void unrest and discord. Celene would also be able to continue to direct Orlais down a path of cultural enlightenment, while also earning more support from the elves through Briala. Together, they'd create an Orlesian nation whose strength lies in progressivism, and create a society where both human and elven citizens can flourish. That Orlais would embrace peace and diplomacy over military expansion under their rule also guarantees stability in southern Thedas, which would go a long way in dealing with future threats from Tevinter, and would make it easier to form a united coalition should the Blight or even the Qunari threaten the south once more.