Welcome!
It sounds like you are giving your son just what I needed as a kid! From the perspective of adulthood, I have some ideas for how to prepare a young me.
CTY doesn't require psych testing, just standardized achievement tests. Homeschool parents can self-nominate, then you choose a test such as the SAT or their own SCAT. Several of these are available by appointment at a computer based testing center. It's a fairly low-stress experience and not terribly expensive.
CTY programs, on the other hand, are expensive - but we found a summer CTY program to be a good reality check for how DD would interact in a classroom environment that was properly paced for her. She had some study and cooperation habits to learn after her previous school experiences. If you would be able to afford a private school, well, a 3-week program is less expensive than a year of tuition... It's also good to have a gifted social experience, especially for a smart kid isolated in a rural backwater. Speaking from my own experience.
Also speaking from my own experience and first-hand observations, students who attended a similar institute of technology with the sort of pre-college experience you describe tended to be lost and underprepared, even while they were actually able to do the work. Junior colleges don't have the pacing expectations of a top-flight school, and it can be quite a shock to make that transition. It was hard for me to figure out how much effort I was supposed to put in, or how to do it; I had occasionally had to study a list of facts, but I'd never had to work to understand anything before. I had never met anyone else who was near my academic level. This was a handicap.
For now, at 10, the junior college sounds like a good plan. By high school - that is, four years before you anticipate college - a more intense experience with intellectual peers will be important. The students who had attended elite summer programs for several years in a row were well-prepared to do their best when they arrived on campus. They were by far the best adjusted kids at the school, and I envied them. CTY isn't the only one of these programs, so shop around a bit if it doesn't seem to fit your son.
