Here's something you may want to read about Esbilac.
LA Animal Watch: Petag's Esbilac puppy milk contains heavy metal copper
Even without the above warnings in the link, Esbilac is not as easily digestible as goat's milk. I don't think you need to wean him off the Esbilac. You could just go ahead and use the goat's milk.
I've always gotten the goat's milk in the can and it is concentrated. If yours' is canned, read the label. It should say to use with equal parts water. Also, if it's canned, shake it very well before opening as the milk solids settle in the can.
When I've used it, I always dump the can with equal parts water in a pitcher and pour a little into a small sauce dish and just add a dollop of karo (about 1/2 tsp) to that. I warm it like a baby bottle and feed the baby. It should be enough for several feedings and you can re-use it but I wouldn't reheat it too many times. You can always give the leftover to Mom if you want. She'll love it.