I am sorry to hear of anyone/thing suffering, I hope things work out for the best, with least suffering for Zap. That has to be tough to deal with. It is so compassionate of you to be so taken with Zap's comfort.
I cannot imagine no vet nearby will care for a goat ....then again, maybe I can ... it reminds me of a vet I called when my son's hamster escaped and got stuck in (and unfortunately consumed!!) some insulation .... receptionist laughed and said it is a $6 hamster, get a new one and the boy will never know. Ha, yeah right, not to mention it is a living creature.
Best to you in dealing with this, and for Zap as well.
PS: BTW, it isn't a silly prayer request
It shows your compassion. A very good prayer request