We put ALL responsibility on each individual. If you have Plague Sickness, it is your responsibility to AVOID the disease. If you have Unbound Plague, it is your responsibility and yours alone to pass it off before you die. Obviously, Ventrilo communication is still preferred and encouraged when you're getting ready to pass it off. However, our policy is that if you're trying to hand the disease off, and the person is running away from you, it is still YOUR fault if you die.
If you're having trouble with the disease at the phase transitions, you should have a warlock get a soulstone ready and soulstone whoever has it. Let them die. Disease goes away. The only time this should be a problem is the second transition.
If you've done the fight in the 10man version, let me just say that the disease is a lot LESS deadly in the 25man than in the 10man. You can essentially let it bounce around several people for several seconds without any care or consequence. The disease can really be in the melee cluster (or, in phase 3, the range cluster) for ~30 seconds before becoming deadly. What this means is that there's no "rush" to get it out of melee range. We run this fight with 8-9 melee. The rogues, 1 ret paladin, and 1 fury warrior completely ignore the disease. The remaining 3-4 melee are charged with getting it out if it targets a melee first. The only big difference in the 25man is that you should pass it off sooner rather than later. 14 seconds kills you. Don't be stupid with it.
In phase 3, we throw the disease in the melee and ignore it. It will kill someone, but it doesn't really matter who.