Gillybob, please don't give up hope. Having read this thread, I can clearly see that you already have quite a number of positives in your favour.
I was in a similar situation to you, went to appeal and won. Do remember that if you decide to go to appeal again that this time it's for one child only - not three.
This was my situation... my husband, parents and I moved from Scotland to the South Coast of England with 3 sons aged 7, 11 and 14. This was a month before the English summer school break as schools go on holiday a month earlier in Scotland.
During the first month, our sons were having a great time making new friends (this turned out to be important) while we were looking around for suitable schools. To state the obvious, they weren't coming from a feeder school. We found a lovely primary school for our 7 year old and again for our 11 and 14 year old only, the entrance year for the 11 year old was refused as the school was full. He was heartbroken. ALL of his new friends were going to this school and the alternative was 5 miles away and it had a bad reputation. The way you've described how terribly upset your GD is at the moment fits perfectly with how he was. So, the appeals process began.
The date of the hearing was three weeks after the school resumed. During that time, my son was at home watching his friends go off to school in their uniforms. I refused to send him to the other school. I knew if I did that they would never change their minds as he would have been deemed to be 'settled'.
I did a lot of research including contacting the schools to find out what time in the morning each school took responsibility for them when the children were dropped off. That was VERY important. I couldn't drop my youngest off until 8:15 because had it been earlier, the school weren't looking out for him. I did the same with the other 2 schools and, cutting a long story short, I would have to choose which child was going to be 15 minutes late to school every day. It's interesting to note that when I brought that up at the tribunal, the solicitor for the LEA stood up, slammed his file shut and walked out mumbling - no point in me being here now!
When I went on to explain (VERY courteously) how terribly distressed my son was and that he was already saying 'I'm not good enough' I could see a few concerned frowns. I also told them how he was naming friends (who went to the school of choice) and saying they wouldn't want to be his friend any more. I told them that I truly believed that if the refusal was upheld, given that he already suffered from lack of confidence that this would become exacerbated and that his ability to learn would be severely compromised.
You already have good reason for an appeal given the transport situation and you have the benefit of the bus driver's support. That in itself should be enough to grant your little GD entry to the school.
There were other salient points but I don't want to bore you to death. You must feel as though you're in 'information overload' at the moment. If you want any more of my ramblings, just say.
When the interview was over, we were asked to wait outside. As I was leaving I said 'please, please say yes so that I can make a wee boy sitting at home very happy - in a smiley way. We were called in ten minutes later and the chairwoman said 'we are very pleased to say that xxxx has been granted a place and thank you for putting forward a logical and courteous case'. I'm not boasting - I'm just trying to get you in the mood to appeal again gily.
Perhaps some of the above may help / maybe not. One way or the other I really hope you can find a resolution for you all. It's all very harrowing for you.