An interesting hypothetical situation....
Let's look at some of the facts. Loghain has been a respected national hero for decades. While Bryce was a loyal royalist, I think he would have believed Loghain when the battle was lost, and they had to pull out at Ostagar.
I would certainly hope, however, that Bryce would talk some sense into the nobility and stop the civil war. Only fools fight over a stable as it burns down around them. The darkspawn are a serious threat, and need to be dealt with first and foremost. As Bryce has no problem with diplomacy, even with those damnable Orlesians, he might be able to persuade Grey Wardens from other lands, like Nevarra or the Free Marches, to enter.
Once the darkspawn are dealt with, it's now the proper time to name a ruler. During the crisis, Loghain appointed himself Regent, which was fine, but I think Bryce would start doubting Anora's capability at this point. Regents are only declared if the heir is unfit to rule. That doesn't look good. Besides, Anora doesn't have a single drop of royal blood. The Couslands have a far better claim to the throne than either the Mactirs or Guerrins, who both try to claim by marriage.
If Howe didn't sack the castle, Fergus is still married. That leaves one child left. If its a male Cousland, Bryce could have him marry Anora, making a compromise of sorts with Loghain and keeping most of the nobility satisfied.
If it is a girl, that complicates things, because Bryce might be skeptical of Alistairs' claim to the throne, which relies on Eamons' word. A female Cousland has a better claim to the throne than Anora does, but Loghain has the loyalty of much of the army....
- Female Cousland marries Alistair. Probably not the best option, because this would upset much of the nobility, who are trying to win the very eligible Fem!Couslands hand. Royalists, however, might see this as the best compromise, keeping a direct descendant of Maric on the throne. This also wins Eamon as an ally, but I personally don't trust Eamon.
- Female Cousland marries someone else. Still going to have Loghain as an enemy, and also Eamon, who is trying to take the throne by putting Alistair on it. If Howe didn't go crazy and murder everyone, his son Nathaniel might be the best option.
- Either Fergus or Bryce take the throne. Bryce is respected by many, and was considered a candidate for King once. The tricky part is naming an heir at this point. See above.