Why can't he accelerate in Science and History? It's an online school (k12.com). Why can't he go at whatever pace he likes? Have you determined exactly where the supposed rules are that are blocking his progress?
Have you thought about purchasing courses individually (
https://buy.k12.com/ecommerce/public/index.xhtml), and seeing if the school will recognize the progress? While the k12.com courses with teacher and credit are expensive, if you get a course with no teacher and no credit (just like a traditional homeschooler purchasing a curriculum) it's just $29.95/month/course, plus the cost of materials. You could gain a year over the summer (in chosen subjects) without missing any material.
Also ask your school about their gifted program. They may be able to get testing for free.
