Hi Aaron,
So sorry about your daughters spinal injury but very happy to hear that the tumor responded well.
As Alex says, nobody has the perfect answer here. But there are some interesting data points.
MSKCC skip transplant and treat with humanized 3f8, hu3f8 has had a very successful phase 1 trial, they found the MTD (maximum tolerated dose) to be so high that they basically stopped trying to go any higher. As a result kids being treated with hu3F8 are able to do this without any overnight stay and get much more antibody than MSKCC were previously able to give the kids with non humanized 3F8 (ch14:18 on COG is also not humanized, only st. Judes had a humanized version). They have about 3 or so years of data with hu3F8 and my understanding is that they are very happy with the results.
This hu3F8 trial is extending to a whole bunch of centers around the US, but I am not sure if it will be available to you fast enough except for MSKCC.
There is a large amount of controversy around one transplant, two transplant vs no transplant. However MSKCC have an unfair advantage in that they have a more intense immunotherapy drug and vaccine so a lot of the comparisons in literature are never able to look at a complete protocol by MSKCC.
I would recommend contacting MSK if you can and at least getting some idea about what they could offer you, they may also be able to manage spinal surgeries and since immunotherapy would happen both earlier and less intensely it is possible you could deal with that earlier under their protocol.
Anyway, I wish you all the best and lots of good luck
Sam