Well, the saga continues.

The school that said they had the WISC III for us to borrow has looked for it and found that they do not have the III only the IV.

DD's principal is not familiar with the IV but is willing to get training on it if we want, but she doesn't know when that would be.
The good news is that she has now taken this quest on as a personal one!

She believes that giving DD the test should be a service that the school can provide, and she is doing everything in her power to make it so. She has called the next BOCES over (located an hour away) and asked their psych if they have the WISC III, or if she would do the testing. Well, it turns out that a tiny district in the next town over from us has changed BOCES to this one that is farther away because they were tired of dealing with the local crap. Which means that the psych has to come our direction every month for meetings in this little neighboring district. She too thinks that our BOCES is being absurd about being afraid of "opening the flood gates" if they test DD.
So, she has agreed to test DD next time she comes out our way.

With this twist of events and with her talking to the little district that switched, our charter school principal is now thinking of switching BOCES too.
As much as I would like to tell you all that we have finally succeeded in getting the test administered - we'll have to wait for a later date for that news. But, at least DD's got her principal in her court and she is working on getting this resolved before school gets out.