Goats and garden fences

My goats are out of control. I have three goats that run loose. My wimpy solar electric fence keeps the horse in but the goats ignore it. I don't want to replace the charger because we will be spending a lot of money on permanent fencing, probably in the next year.
My garden is 54x80 and I have cattle panels around it.
My problem is that I want to plant a number of tall crops and vining crops around the edges of the garden since it makes the most sense in my layout. Sunchokes,sweet potato,squash,okra,amaranth,artichokes,cardoons.
Last summer I planted amaranth and okra about 2 feet from the fence. The goats climbed the fence and stood on it until they bent it over far enough to basically climb over. They also stuck their heads through to eat everything.
I can stop the heads being stuck through by adding some wire ( I have some scraps) along the fence but that doesn't stop the climbing.
can anybody think of a plant that is tall,sturdy,attractive to goats and that horse will ignore that I could use as a boundary outside the garden?
I am beefing up the fence with more and sturdier t-posts. My father suggested adding a wire fence outside the garden fence but that would involve a lot more t-posts and I'd rather not have that expense if I can prevent it another way.

Welcome to goats.  And a great big warm welcome to Permies.com.

Goats are a challenge to be sure.  They eat the fruit trees, play trampoline with your car until the roof caves in, but most of all, they will find a way into any place you don't want them to go - given the chance.  I feel your pain.

Knowing that goats can be such a huge challenge, I tried to make certain they were the last animal I added to the farm.  I knew I couldn't handle them until I had the infostructure in place... but then, there was this one goat on the truck to the butcher that I just couldn't pass by, so I brought the goat home before I was ready...

For an electric fence to work with goats it has to be ridiculously powerful and the goats need to be trained to recognise and respect the electric fence.  This can take up to a year, depending on the goat, but once they learn, they respect the electric fence even when it's not hooked up to the charger - so long as there are refresher courses every few months.  Once the goat has learned not to fear the electric fence, it's a lot more difficult to train them.  

Is it possible to set up a more permanent pen/pasture for the goats?  It's funny, but mine seem to be happiest with quite a small pasture, so long as I take them for walks a few times a week.  I set up their fence for very little money - the posts are mostly reclaimed 10" posts (about 6 foot high - sunk in the ground two feet or so) and logs from trees that were about the right size.  The boards are wood from old pallets.  And on the inside of the fence, I stapled old wire fencing that I reclaimed from around the farm.  Basically, it was the cost of the hinges for the gate, the staples and a couple of screws.  The goats can get out of their pasture, and do about twice a year, but only when they aren't happy.  We have a good perimeter fence, so I don't mind terribly if an animal gets out of their pasture as they are usually too stressed out to get in the garden.  They only do it when they are scared or unhappy so if someone's loose, I know I need to do something about it right away.  

Some people chain up their goats.  If you have one or two goats, this might work.  I'm not a huge fan of this, as it's expensive to buy a strong enough chain and I imagine the goats don't like it - but they never show any sign of not liking it.  This could be a temporary solution for a few weeks.  

I tried it one year where I had the goats in a large area, next to the garden, and fenced the garden like I described above.  That lasted all of a week before the goats learned how to climb into the garden.    So then, I fixed the fence and tried the same set up with the sheep.  That lasted a month before they found their way in.  This has given me the theory that it's easier to fence the animals into a pasture than out of the garden.  

can anybody think of a plant that is tall,sturdy,attractive to goats and that horse will ignore that I could use as a boundary outside the garden?  

That's a  neat idea.  I hope someone here can suggest something that might work.  

I have an idea of a plant: Mexican sunflower.  I am not sure how hardy it is to cold, but its otherwise pretty hard to kill, and it makes both an excellent hedge and useful goat fodder. (It has medicinal properties as well).  We use it around the property boundary, roadsides, and in other marginal areas.  I don't know if horses will eat it. I know the cows ignore it unless they are extremely hungry.  If it gets too tall you can cut it back, even to the ground, and it will come right back. The goats can strip it bare, and it will come right back.  It might work to add a boundary of Mexican sunflowers around the exterior of the garden... But then again, they may find your veggies too appealing, and plow through the hedge.

Try planting luffah on the edges. The one year I grew it in W. TN there was a drought and deer were getting into gardens. Not ours. Aromatic herbs repel deer, and since deer are related to goats, they may work.

To plant something outside the fence that may slow them down, they like roses, raspberries, and blackberries. They love them, so plant them thickly. They're also good for them. You might even get a crop off of them.