Our montessori school uses the MAP tests liberally - three times per year for everyone - for grades 3 and up. For grades 1-2 they recently started using STAR tests. While I think both of them fall into the category of quick-and-dirty, they might be a place to start before you spend on formal achievement testing, if your school is willing to do them.
I hope your child's teacher is keeping close track of the works he has done. If they're too easy, why don't they skip ahead and try something much harder without requiring a show of proficiency first, just to get a feel for where he's at? I think that if the montessori teacher thinks about it carefully, they ought to be able to come up with a plan.
What age/grade level is your child, and where do you think he's at (with math/reading)? Figuring out what he can do with math, for example, shouldn't really be that difficult, though I do understand what it's like to have a child who pretends not to know anything and who is afraid to try any work that might require him actually having to use his brain (due to both fear of failure and exertion of mental effort in an otherwise too-easy world).
Does he ever ask for specific works? Is he afraid to ask for some reason? Does he need a lot of direction? Different kids approach these things differently. How about his teacher - is s/he willing to demand more of him, or is she wedded to child-led work selection? I guess I'm trying to get at the root of the problem....
As for the testing, I'm not sure what the difference is that you're asking about - the private school psych vs. a neuropsych - they ought to be able to do the same thing, though a neuropsych who specializes in gifted/twice exceptional kids may have more expertise in the test administration and analysis that would benefit your son (if the private school psych is more accustomed to "average" kids). If the cost is similar, I'd definitely go with the neuropsych.
just thinking out loud...
