I am so sorry to hear your terrible story. I hope the dog is responding better to the drugs. Please let us know.
From what I understand, the airlines can not open the cages to let dogs out, unless othewised arranged.
I think the suggestion to take the last flight out and then overnight and conect in the morning is a good one. I would try to re-arrange your flights home (not sure how long you are away for).
I have also shipped a dog cargo, and they are very careful with the handling and transfer. I think maybe better than when they are traveling on the same flights with you.
I wish I could give you better information, but we are all thinking good thoughts for your dogs.