Can you not take them yourself? As long as you do not keep your goats for business you do not need one of the certificates for competence - I have taken goats (my own) from South of Scotland to near Land's End in Cornwall with no problems/questions asked - and I did fill in the forms correctly. Several times.
If you don't have one - hire a small van, lay it out with a tarpaulin, nice absorbent bedding, or see if you can hire a livestock trailer, even a small IW P6 (can be towed behind most cars) will be big enough, if you don't have your own. A couple of breaks for feeding and water (take buckets etc with you), plus have a hayrack up, and you are good to go. Subdivide the trailer into two pens if possible, so kids are separate form adults. If you are worried about heat etc, set off in the evening and travel through the night.
You may want a friend or other driver to accompany you, though I have done the journey by myself and slept ovenright in my van on the buyers field....
But then I do love a long drive in my van....