As with the 2 DR from different players, I would argue for them to only be applicable to a player's first battle and all stack. To my mind it's still a question of whether the DRs stack, not whether you can delay them over multiple battles. It's arrangement has all DRs applying to the first battle the target engages in, but to not allow the stacking would negate the experience spent and trying to jimmy with the arrangement allowability opens a can of worms.
Stringing them out over longer periods strikes me as hamstringing the player rather then letting them fight out one very one-sided battle and then moving on with the game. You may even load them up against Player A and end up not fighting that battle against A, someone else reaps the benefits of the Raids.
However - barring an amendment from some of the Mongoose dignitaries, I would also put it to a vote in my local group to settle it decisively.
