One Lady, Five Beastmates, Zero Affinity?

Cara finished her hundredth mission and was supposed to be sent home to Blue Star. The system misfired and dropped her into a world overrun by zombies, where men can shift into beast form for the strength it gives them and pay for it by sliding toward a madness that burns out the mind. Only a woman can calm one back down. The body Cara lands in belongs to the youngest daughter of the Duke of the North, a spoiled girl who kept five capable beast husbands and took a whip to them whenever their condition made them difficult. All five of them look at her with hatred and something closer to murder. Cara starts from below zero, with the dead pressing in on the territory and a system still handing her tasks that require winning over the exact five men who have every reason to want her gone.