sd, fwiw, my kids are also not tested, nor have we ever seriously considered applying to DYS. And yes, you have every right to be here!
WRT skipping alg II for precalc, it's a useful perspective to remember that precalc originally was basically a review class inserted because so many students weren't prepared to go straight from alg II to calc, so skipping one or the other doesn't seem like it should be a huge issue. (One of mine started DE calc half-way through a year-long precalc course, with successful outcomes for both.)
On the question of upper level math: our experience has been that the DE math courses have been a much better pace for our children than the supposed high school equivalents--if they are true college courses and not designed for high schoolers in early college programs. Which makes sense, since AP Calc AB is only one semester's-worth of first-year college calc. And for CC vs uni, it's really been more about the individual professors than the institution (keep in mind that a lot of the same professors are adjuncts/affiliates at multiple post-secondaries in a given region--hard to make a living as an adjunct professor at just one job). You might run the names of some of the nearby college instructors through RateMyProfessors to see if you can get a sense of their quality and rigor (not always evident purely from the ratings; DC loved the math professor that a lot of non-STEM majors described as too hard, precisely because so much higher-level conceptual instruction was in the course).
On college prep: we have a similar philosophy regarding selective universities. We certainly have not discouraged selective unis, but with offspring who are likely headed to graduate school, our view has been that the quality of undergraduate education, including access to research opportunities, internships, and actual tenured faculty, is more important than the name brand (not that these are not correlated to some extent--just not 1.0). And childhood is short enough as it is, without curating all of their experiences.
With regard to the right choices/options, there's a surprising amount of information you can find on places like the College Board's college search site. You could check out some of the college prep forums, too, but I haven't spent that much time on them, so others are in a better position to say how valuable they are.
In terms of BTDT, DC was homeschooled for high school, with home-based programming through 11th grade, and then a full college courseload of dual enrollment for 12th grade. Admitted into uni as a first-year, but matriculated directly into sophomore status.
Currently DC is at a moderately-sized regional state uni of unremarkable reputation, but has had really excellent instruction, and exceptional mentoring, with faculty recruiting DC for multiple stipended research and teaching assistantships, including recommendations for nationally-competitive positions, opportunities to present original research at the annual conference for the major organization in the field, and fairly high-contact mentorship surrounding DC's honors research. Even faculty in DC's additional interest areas (not formal majors) have offered very specific, individualized attention and direction. Obviously, YMMV, but the point is, we certainly could not have asked for a better set of educational experiences--including the kind often favored on grad school apps--from many more selective institutions.
But then, my DC had no special interest in a selective school, and had already made that clear. It might not be a bad idea for your DC to start investigating categories of universities casually now, more to have a sense of what's out there, and what kind of settings might suit him. It may be that certain qualities really matter, and others really don't. The content of those lists may help redirect college prep--or confirm that your current approach is right for your child.
