Welcome AMD!
I read your post with great interest as I also have a 5 year old (she'll be 6 in January). We managed to do early entry to K, at age 4, so she is in first grade this year. Like you, we do not have the financial resources to choose private school at this time. We had to switch schools early in the year (within our same district) but luckily we now have a wonderful teacher who is doing the best she can to work with DD5 and keep her challenged.
Your post jumped out at me because of your son's teacher saying she'd never seen a child like him. Just before Christmas break, DD5's teacher told me the same thing. She said "I've had a few highly advanced children in my class before... but I've never seen a child like your daughter." It's hard to know how to feel about a statement like that!
As for your questions, I think you're wise to pursue testing through the school system but also seek outside resources. If you have any reservations about the results/interpretation of the school's testing, you can always do independent testing as a means of comparison.
You're very lucky to already have a K teacher who recognizes your son's giftedness and a school district that seems willing to provide accomodations. If possible, try to "hand-pick" your son's teacher for next year and talk to her ahead of time to be sure she understands the situation and will be supportive of what your son needs. Don't hesitate to ask exactly how she will accommodate your son so he will actually learn something new and not have a wasted year.
Best of luck to you, and keep posting so we know what happens!
GG
