As usual DeeDee and polarbear have addressed the main issues. I will add a few things based on my experience with my DS8 in your state.
First, the school is jerking you around. Hinting that you should go see elsewhere and having as an accommodation that they can kick your son out whenever they feel like it is a violation of the law. Even if the school is a bad fit and you end up going elsewhere, they are supposed to provide him with a free and appropriate education.
Second, while the recommendations from the local gifted center to first try getting an assessment from the school might be a good plan for a gifted child, you have enough red flags for 2e that I wouldn't trust the school. In CA there are no obligations for gifted services, so id'ing him doesn't cost the school much of anything (and might help convince you to go look elsewhere). But there are strong incentives not identify a child as special needs (since that requires providing actual services), especially if the child is doing OK academically (as defined by meeting NCLB goals) and is not too disruptive in the classroom (or can be handled by having mom deal with it). It is much better to get an assessment from a trusted specialist on your payroll who can help you figure out what your child need and also help you push that through the school. Lastly, assessing 2e kids is tricky (strengths hiding weaknesses) and standard assessment plans might not show either the gifts or the weaknesses.
The principal at our school recommended I get a private assessment after asking me if we had good health insurance. I was offended/horrified (the school has 75% low income families who can't afford to drop 3k on a neuropsych assessment, although we eventually did it), but by first asking that the school do their job the way they were supposed to we lost two years. I just finished digging myself out of that particular hole (DeeDee, polarbear and everybody who answered that first post of me way back when, we finally got an IEP 2 weeks ago!).
Anyway. The legal framework in CA is formal request for an assessment (in writing!) sent to principal, copy to SpEd Head for your district. The are form letters available online. The school has 2 weeks to convene a SST meeting to draw an assessment plan (or deny the need). I would recommend talking with a specialist beforehand to make sure they assess areas of weakness properly, despite his high intelligence (as an example my AS son does OK to great on standardized speech assessments with adults, and gets very decent scores (+1SD) on the most common tests of pragmatic language -- it took going for some obscure, specialized tests and doing in depth observations of interactions "with peers in a naturalistic setting", a phrasing recommended by his private psych and inserted in the assessment plan, to unveil his issues in a way that qualified him for services). Once the plan is drawn they have 60 days to evaluate. Expect them to take every day they have (everybody is underfunded and overworked). After that an initial IEP meeting will be scheduled, where services will be proposed (or refused).
I would recommend you talk with an advocate to get a feel for your school/district, talk with a neuropsych (or that gifted center) to get a list of tests that could be used to assess your child (if it is not too late for that, since it sounds like you signed the assessment plan?), and get on the wait list for a private assessment with a neuropsych that understands 2e (if you can find one).
