I can't imagine that the school would accept WISC and not accept WPSSI, but you never know until you ask. It is certainly worth it to ask what the 'work around' policy is.
If you want her to have more Math, can you afterschool math for 2 months, say, just to get her over the hump?
And if the teacher is going to send home a second set of spelling words, I'll bet the teacher would love to know that a new group of harder words are needed.
I'm not really buying your interpretation of the psychologist saying that gifted school is the only way to go and you are doing her great harm by not providing her with that. It just sounds too much like the 'gloom and doom' we parents are so susceptible too. And if the psych did too say so - I'd argue with her/him as well. There are just too many ways to do parenting right.
((Hugs))
Grinity