Here's one way to look at it, during the olympics there was an article
on one of the news sites about the cost of raising an olympian. I'd put
money on there being many potential olympians out there who's parents
chose not to spend that money or couldn't, but didn't push and scream
for help.

So you have to figure out what your aims for her are, she's obviously
very bright, probably even super bright, but education isn't necessarily
the way that you turn that potential into being a functional adult,
which I'm presuming is the ultimate aim for her. I don't know enough
about the school to know how it would help her, and I do wonder if some
of the problems you've identified about the parochial school would still
apply to the dream school, chances are, even there she'll be way above
some of he students and what do they have in place to deal with that?

If they can deal with that, then maybe that causes another problem, that
she won't learn to work for something, to be independent, to direct her
own learning etc again, I don't know the school, so maybe it will teach
her those things.

Me and my sister are both bright, I don't know how that compares to your
daughter, but we were definitely a bit precocious! But we have different
personalities, at elementary age I got my schooling in public school and
I did fine, mostly being one classe ahead of my age. My sister went to a
private school that was probably somewhere between the parochial school
and the dream school, she also did fine, but we wouldn't have done fine
the other way round. I think the teachers at my sister's school would
have lynched me! My teachers at the public school dealt with my by
handing me an old maths book lying around and letting me stick my nose
into that, it's hardly the perfect way to do things, but I did fine and
I think did learn a lot more self study skills than my sister, which
was something she struggled with for a while.

I think I'd be inclined to try public school and see what happens, if
that keeps you a SAHM, that gives you the chance to spend time with her,
supplement her education, encourage self directed study etc, whilst
saving money for if the time comes that the dream school does become the
right thing for her. I think that a younger child is much more adaptable
so as long as they are watched carefully, which you can do when they are
younger I don't think public school versus private school makes such a
difference as it can do when they are older. FWIW, it's very common in
the UK for a child to go to school within the state system and move over
to private at 11, 13 or 16, when the parents do have more of an idea
what's best for the child and can then choose a school that's good for
them.

Cheers
Anne