Mr. Miller,
Killing the dog is not the answer or an option I would personally pursue. I mean, after all, you did let the dog out even if accidentally, and as a result of your lapse in supervision the dog, of protecting the dog...
That out of the way... You asked the following questions:
QUESTIONS:
1. Can training eliminate this behavior?
Eliminate? No. But training creates conditions of conditioning and more behaviorial certainty. I speak from experience, and experience with an incident very similar to yours.
2. What sort of training would it require?
A lot of training and dedication to working with the dog. The amount of training and the depth of training has more to do with your willingness to have a well trained dog - any dog. You should understand that without training, and confidence in that training, you can experience the same behavior with almost any dog.
3. Can this training be accomplished by me? Quite frankly, I cannot afford specialized classes.
Of course it can be accomplished by you - if you want to, and you want to spend the time. This site offers all kinds of training aids; and there is always the books by the Monks, and by Ceasar. Bluntly it won't require super specialized training because I don't think you have anything other than a dog that needs training, exercise, rules, boundearies, adherence to commands, etc. In other words, he needs the same effort any one would spend to train their dog well.
4. Is there a DVD that specializes in this problem?
You have come to the right site. Absolutely. But you should not think you have a man killer on your hands. You have a dog that needs training. Lots of products here that will help you understand training and then the execution of training.
5. Can an electric fence deter a 90 pound GS intent on going after another dog or person passing by the house?
I'm a fan of 5' or 6' chain link fences, myself. People have success with the electric fences and collars - they are just not my style. And a well conditioned command set can and will pay off as much as a fence. I use a fence to keep the riff-raft out.
6. Any other advice would be greatly appreciated.
Educate yourself. Before you can train the dog you need to know how to train the dog. The dog will do what you train if you are fair, consistent, patient, not revenge driven, are rewards driven, are not given to yelling, do the same stuff tomorrow you do today, etc.
It is absolutely your responsibility to protect your dog. You need to know where the dog is when you go through the fence gate. You need to know where the dog is when you open the garage door, or if the garage door is open when you go into the garage. You are the human, you reason, you are rational, you can plan ahead... The dog is in the moment.
Your first object might be to train a 'drop-dead' word, like "NO" or "DOWN" or "COME" that will stop the dog in a heartbeat and redirect its attention to you.
Contact the person injured. Be solicitous. Offer to pay any medical bills. Deal with the dog police honestly - tell them you accidentally let the dog loose. Explain you are undertaking a rigorous training effort.
And continue to post here and get better advice than I offer.
You are not the first person who's dog has injured some one. One of mine did when it was allowed to burst through the gate and get too far ahead. I've still got the dog, and it visits senior citizen residences. Good dog - bad handler.
Don't panic and think in extremes. Train yourself. Train the dog. Good luck.
Mike A.
"I wouldn't touch that dog, son. He don't take to pettin." Hondo, played by John Wayne