I have no idea whether dog psychology works on goats, so please ignore me if this is a stupid thing to say, but with dogs my favourite technique is:
When they pull, you stop. When the lead is loose, you walk on.
When they pull, you stop. When the lead is loose, you walk on.
When they pull, you stop. When the lead is loose, you walk on.
repeat until you only stop because you want to. If you are 100% consistent, the first walk takes an hour and doesn't get to the bottom of the garden

but by the end of a week they should be walking nicely on a loose lead.
I don't use any words at all while doing this; I find while they're learning, any word that means 'get moving / walkies' makes them so excited they inevitably lunge forward - so then it meant "get your throat tugged and Mum stands like a stone with an expression of thunder" - result : confusion and frustration.
If you use no verbal signs at all, they get the message pretty quickly.
I look forward to learning more about goat psychology...
