[This is more commenting on the options you've got than offering new ones, sorry; I realise it's not what you asked for.]
LOL! If I weren't up for that, I wouldn't ask on the internet.
Why do you say homeschool for a year? Just in order not to look beyond next year, or do you think middle school is going to be much better for her?
In order to not look beyond next year, for the most part, but I do think that middle school will be easier than elementary - you get more-interesting subject matter, from teachers with an interest in that subject, and limited ability to set your own schedule. Plus there's ability differentiation to some extent, and the other-parent rumors are that the ability differentiation isn't "more homework for smarter kids."
How does she (and how does your DW) feel about that option?
Honestly, there is no parent support for an additional full grade skip. There's no way to undo the skip (we've asked), and we're concerned that a second skip would limit her choices for college. (Either because the school would think she was too young, which is sort of what happened to me, or because she would feel unprepared to live semi-independently thousands of miles away from us.) For her first skip, she was well-qualified using the IAS with some conservative guesses for IQ and achievement; for a second skip, she'd be marginal even with a high guess for IQ and known-good achievement scores, entirely due to factors beyond her control, like height and skipping the transition year. DD vacillates between wanting a full skip and not wanting one.
Can she take both the tests that would let her subject accelerate to 6th in maths and the ones that would let her go to 7th, or do you have to commit to having her take one or the other
We'd have to commit to taking both, so she'd take the 5th test, then if she passed it, take the 6th (probably the next day).
Are you basing your estimation that she could go to 6th but is borderline for 7th on a careful look at the syllabuses?
Yes, although the syllabus is not written in a particularly helpful manner. For instance, you might remember from elsewhere that I had difficulty finding examples of addition of fractions with unlike denominators, and looked at the pacing guides and sample end-of-year tests, only to discover that that skill is apparently not tested! Or at least, not sufficiently heavily weighted in the test that you'd get many problems - the sample tests are about the same length as the real thing, and contained no problems on that topic.
I've given her pieces of the end-of-fifth sample test, both sections I thought she could do, and sections I thought she couldn't. And she got all the problems I gave her correct, although there were a few she balked at, saying there was no correct answer or she didn't know how to tackle them - but when I encouraged her to give it a try, she did just fine.
The only reason I'd consider a placement in 7th, rather than 6th, would be to get pre-algebra, rather than basic math. I don't think it would necessarily be a better placement, though, either academically or socially.
I don't know how it is in your state but I think this is the stage where there starts to be a fair amount of Stuff in US maths classes, i.e. it'll be more important than it was with her earlier skip to make sure she's been exposed to everything she needs.
Because of the nature of the testing, I don't know that we'd need to take that into account in deciding whether to test. I worry more about conceptual gaps - like the decimal multiplication problem she solved correctly, then asked whether you counted from the right or the left when picking where to put the decimal point. (Upon discussion, it was clear she did not understand why you moved the decimal where.)
If she doesn't full skip this year, do you think she will probably be doing it next year (skipping 6th)?
No, because we don't really want another full skip. I think if she didn't subject accelerate for the coming year, she would for the next.
I don't think it would make much sense to subject accelerate her in science without also doing so in maths.
Agreed - and DD doesn't particularly want a science acceleration.
At least in principle there comes a point where the science needs the maths anyway, so getting science ahead of maths formally requires a way to undo that later. And it's pretty clear (isn't it?) that one year of subject acceleration in maths is within her capabilities anyway.
How does she do if you give her
a JMC paper for example?
I have insufficient math background to figure out how to begin to tackle most of those problems, so can't scaffold them for her. And she's been underchallenged long enough that she's unwilling to attempt a problem that she can't figure out how to solve in a minute or two.
