Well crud. That's amazing that the cartons spoil that quickly. I would think that you could freeze the goat's milk when you get it and just un-freeze what you needed at each sitting... but I'm no expert. But that's what I'd do, I mean if you freeze it right when you get it, then when you unfreeze it I would think it would still be fresh. Maybe someone else will chime in.
I have no idea about the evaporated milk, again, I hope someone with more experience with that can chime in.
I would think if they're not wanting to drink from a bottle with a glass dropper, then you probably wouldn't have any luck with the type of bottle I have. Mine's just the glass portion of a baby-food jar (minus the lid), and the Ryerson water bottle stopper and sipper tube... I got them from a breeder... they're used here in the US (with a bigger bottle of course) by people who use breeding runs for their chins... I'm not sure where you'd find that sort of stuff by you. I would think, though, that if they're not going for the glass dropper, then it wouldn't do you any good anyway, because that bottle has a glass dropper...
I know you said you made a bottle with a glass dropper.. would it be possible for you to make a bottle with the rubber nipple, maybe that would help you with feeding? I think, to some extent, if you make them, they will drink from whatever you give them. I find the glass bottle the easiest, because unlike syringes, you don't have to refill it... but at the same time, it was a bit different from a syringe, and so when I first switched the babies over to the bottle, they didn't take to it right away. But eventually, they got hungry, and I didn't go back to the syringe, and they figured out how to drink from the bottle. I think that probably would work for your situation as well... you know, just keep at it with the glass dropper (without going back to the rubber nipple) and sooner or later they should realize that if they want to eat... they're getting it out of the glass dropper.
Good luck.