I know what you mean Justin. When an animal is destined for slaughter, you know all its life that that's what going to happen to it, but when it dies unexpectedly, that's more difficult to deal with.
The vet call-out fee seems enormous - here it's about £30 I think, although we've not needed a visit recently. If your animal is OK to move, then it's much cheaper to take it to the vet, rather than the vet coming to you. So a trailer or the back of an enclosed pick-up is fine, as long as you lift the animal in gently.
For meds on hand, we do always keep AntiBiotics - one long acting penicillin based, the other LA oxytetracyclin, but this is for sheep - for pigs the drugs needed may be different. In a previous life I was a nurse, so our vets were happy to let us keep the AntiBs at home, and to decide when to use them. We always buy from the vet, including the syringes, needles and sharps box, partly so we are supporting an important local business, but also so the vets know they are our vets and will respond promptly if needed.
We rarely use the AntiBs, but they are there for an emergency - which will inevitably occur at 11pm on a Saturday. We don't keep pigs any more, just sheep and poultry.
How about arranging to visit your vet to discuss a health plan for your animals, and raise the question of keeping certain things on hand at home, and see what she or he has to say?