While I agree with most of your post, this part;
Your little buddy has lost all his means to escape the aggression with his fins gone. And will be the easiest target. I would remove all the barbs from the tank and relocate them. To give back a much needed calm environment for him, I never punish the victim. But I would gladly use a kakivac to remove the aggressor if needed.
It's not about punishing the victim - I say move the cories to a hospital tank because that cory especially is in a life-threatening emergency situation right now, and moving him (with his cory friends) to a clean fresh container that's more sterile will reduce the chances of infection, make it easier (and cheaper) to medicate, rather than medicating the main tank, and a hospital tank/clean new storage tote isn't going to be harbouring all the nasty bacteria and fungi that the main tank and it's gravel substrate has. He needs lifesaving attention first, then s/he can worry about finding someone or somewhere else for the tiger barbs while the cories are in intensive care, so to speak.
Also without knowing anything else about OP's tank besides their suspicions about it being the tiger barbs, which yes, can be brutal - without knowing the other stocking, there might well be more than one culprit finishing off what the barbs started, or vice versa. If they also have a red-tailed shark or something attacking the cories, then removing the barbs isn't going to solve the issue. Even generally peaceful fish will often target, peck at, and generally be horribly aggressive and mean to a sickly and dying fish, even if they were happily part of the same school previously.
I haven't looked for scientific backing for this theory yet, but I've witnessed and heard about it happening enough times to know how it's a known thing, and I suspect it's a survival instinct, just as has been observed in countless wild animal species. Weak, sick, vulnerable animals in the wild attract predators. It's why most animals hide visible signs of pain for as long as possible. Once hungry predators arrive, attracted by the scent/motions/chemical signals from the sick animal, all of the others are now also at risk too.
It makes sense to drive the sickly one away, in the hope that the rest of the group can escape downriver. When that happens in the wild, the sickly one then has the chance to hide, and potentially recover, depending on what ails them. Or they get eaten, and the circle of life continues. But in a tank where the others are trying to bully and peck at the fish acting like a beacon for predators to drive it away, it can't escape. Another reason is to prevent the remaining fish from eating the body of the sick one if it does pass away, just in case the illness was something infectious.
So hospital tanks aren't about punishments, just emergency medical care. Once the cories are out of the main tank and safe, and being medically treated, even if that's just with a clean environment and water, then the main tank should be assessed for suitability for cories, taking the whole stocking plus gravel into account.