Thank you, everyone! So very helpful, and I really appreciate it!
FWIW, in the meantime, I took a look at online college offerings of the Coursera etc. type. These are (IMO and IME, when I've looked at courses in my field) often not as rigorous as real college courses, but they provide something like 1/4 to 1/2 of a college course, and so are intellectually serious in a way that I am finding (and thank you for confirming) the HS classes are not.
Two I found that look especially good, in case it's helpful to others. (My thinking is that these might, with a college textbook, constitute a good standalone course OR might supplement a HS AP or Honors course):
Coursera Welcome to the Modern World: Global History Since 1760 -- 13 lectures, taught by a UVa historian, with each week covering a span of time globally and thematically
Learner.org (this was new to me, but it's the Annenberg Foundation) Bridging World History -- 26 thematic units, including lesson plans. Columbia lists this course as a resource for college students in history, so I take some comfort as to the quality. The lessons I looked at were good but doable for an intellectual HS kid.
