Believe me, if a pup is shown negative behaviours, teased or is afraid it can start much younger than that. This is why it is so important for any pup to be brought up and trained properly and shown security from 8 weeks of age, it can damage them so much. 

My 6 months old bitch was a little sod to start with, she really would sink her teeth into everyone, and it wasn't due to lack of socialisation or fear, it was just sheer bloody midnedness. <grin> I've seldom seen anything so angry -and so small.
I'm usually one for doing everything the kind way, clicker etc, but with this girl, I had enough. She wasn't scared at all. So the next time she bit me, I picked her up and held her in the air until she calmed down. That's all I did, held her, but by her scruff. (We ARE talking a 1 kg dog here! Had she been bigger, I'd NEVER have done it.) She never bit me again. She then tried the same thing with my kids. After they each told her off just the once, she stopped biting them. We then had a dog food rep visit, Pap pup jumped on her lap, when the rep was about to leave she picked the pup up and again she sank her teeth into the nearest hand. (Thankfully she was teething then so didn't have many teeth!) Now this was an experienced GSD breeder so she just laughed at her ("I've dealt with dogs much bigger than YOU!") and told her no and put her on the floor.
But once trained, they are so loyal and so cuddly and friendly I can't imagine anything nicer. Training classes is a VERY good idea as they also very often get aggressive towards bigger dogs unless they learn to be around them.
but I'd just like to air a little caution, your experienced with dogs, and you did it the correct way calmly, without shouting or showing any negative emotion whilst doing it, you just held her in the air, keep your arm still to show you are the authority here and it worked very well. 

> are quite hopeful that if we address this issue properly we can sort it out
The poor little thing has had a rough start and nobody (before you) has taught him how to behave, he'll get there. I took on a 4 year old dog (from a rescue centre), he snapped at my youngest child over food, we cracked down with training, and he has never done it since (he's now 14yrs old).
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