SQ will be fine. It sounds like that's what the needles are for. When I was giving fluids to a sick dog he would just stretch out on the floor while I rubbed his head. Goat is probably not going to be as cooperative. Might be good to put him on the stanchion. As best I remember it only took about 15 minutes or so, but I can't remember if we did the entire bag at one time or broke it into twice daily...
It would make a big soft lump under the skin, but it would absorb in fairly quickly.
Fingers crossed that he's going to come around for you. If not, it's not for lack of you trying. You deserve a hug!