When I hike around my 3 + mile block with my goats I have to have them on leads for part of the trip. It is about .2 miles down to the stop sign and then I have to turn left onto a fairly busy road and walk on the wrong side due to the fact that the right side has no shoulder and the wrong side has a great, wide shoulder. Still, there are cars and semi trucks exceeding the speed limit by a LOT on that road and it is a scary three tenths of a mile for us. So from home to two tenths of a mile past this section I have to hang onto my 6 packers to keep them safe from cars and visa versa.
That being said, I usually don't exactly string them, I hold the leads in my hands and they come along with me.
Holding 6 lead ropes is perhaps not very fun but my goats are so used to this little procedure that they seldom make the ropes tight and while they do move back and forth a few times and I have to move the ropes from one hand to the other, it all works fairly well. As many folks have stopped to point out to me, my goats walk better on a lead than most dogs.
There is an order and I know which goats to put with whom.
On the trail I'm hopelessly lazy and when we are doing training hikes I sometimes don't even have ropes for my goats, or halters but some have collars. I carry 2 lead ropes in one hand, a bonk stick in another and off we go. They are such a bonded herd that if any danger happens they cluster around me and our LGD, Whitney, does her thing.
The bonk stick (a nice, stout, ax handle, I've had the thing for years) is for strange dogs or humans, NOT for my goats!
All I can say is, talk with your rangers and explain why stringing goats is not a terribly safe thing and that loose goats will follow and will do less damage to themselves and the terrain than strung goats.
I'd go with just 2 or perhaps 3 if they have to be on a line the entire time more will just be trouble should a dog come up and cause them to cluster about you. Explain this to the ranger, that goats, when scared, will run to you and cluster about you to try and ward off the threat as a group. If they are strung together your goats are in danger from dog attacks and you are in danger from all that rope!
Also, find a place where they can be loose and walk them there instead.
Charlie Goggin
Lightfoot Packgoats