- be a normal 5th grader and assiduously afterschool (DD suggested this one; she says school is less boring if she's got something to learn after school)
This one sounds attractive as setting up for a grade skip later. On the other hand, there's no reason to delay a subject acceleration in math now, and she might be able to assiduously study up on social studies enough for a skip over the summer.
- full grade skip to 6th (possibly not within her abilities, since Social Studies in 5th is all US history, and we've intentionally done no work in that area)
I'd try for this by cramming history over the summer. What's to lose? You could fall back to a subject acceleration in math.
- subject acceleration to 6th in math
I'd try for this at the very least, unless you firmly resolve to homeschool her next year. There's no point in stunting her math growth for a year, or even in having her completely waste her time in math class while afterschooling.
- subject acceleration to 7th (pre-algebra) in math (a stretch, but likely not impossible)
I bet this might make her really come alive, as long as you've prepared her well enough.
- homeschool for a year, possibly with the addition of outside tutoring
I guess this might work. I usually worry about increasing awkwardness with the social group unless it's on the cusp of a move or other change in circumstance. Here, I guess if you're considering a skip, the homeschooling year might help you prepare her much better than afterschooling-- you could probably cover multiple years' worth in all subjects in the same number of hours per day or less. And if she's to skip, it will shake things up regardless.
What I might do is get several irons in the fire-- request end-of-year testing at the start of next year if you decide to go for the skip, request the subject acceleration, etc., then plan to homeschool if things don't go your way.
