The Swedish rules support your second alternative. My translation: "during the coming round, until it is your turn again". And since the rules were written first in Swedish I'm taking it as the intended rules. Now, a better way to write this would have been "for the remainder of this round, and until your turn the next round". There are no mentions of any way to prolong the duration, so it is safe to assume that you have to spend another long action and more WP (essentially just casting it again) if you want to have it last another round.
I do agree that a feint or swapped initiative seems to be able to prolong the effects by moving you later in the initiative or shortening it by moving you forward in the initiative. But I dislike this. It is a warcry after all, and not a prolonged hymn. The effects should be in the form of lingering inspiration (or fear in rank 2) and I would house-rule them to end on the next round at the initiative you had when you cried.
I disagree with Fauns interpretation that reacting to an attack (or even simply being the target of a feint) would stop the effects. The talent states that it last until your next turn, and making a reaction is not the same as taking your turn.
I do think it's a really cool idea to let the cry continue somehow and having to power through incoming attacks would make for some really cool fighting bard gameplay. But I think it is important to separate the discussions of what the actual rules say from discussion on cool house-rules, otherwise the discussion quickly devolves into nonsense.