Are Mathematics graduate programs open to admitting a student out of high school with graduate work?
I know of one case in which someone went straight from high school into a graduate program, so it is theoretically possible if you can find a university that agrees.  However, it's almost unheard of, and it would be a bad idea for just about everyone (even setting aside the question of whether undergraduate education provides any benefits beyond preparation for graduate school).

What I assume is that you'd like to do important research and are looking for preparation that will help you accomplish this goal.  The minimal standards for a Ph.D. are actually pretty low, and you can squeak by without knowing much or doing impressive research, but this sort of dissertation will set you up for career failure.  Instead, you need to enter a strong Ph.D. program, ideally one of the top ones, and really excel.

It sounds like you've completed enough courses for a minimal undergraduate degree in mathematics, but probably not enough to be competitive at a top grad program.  The applicants at these programs have generally taken a more extensive and rigorous collection of undergraduate courses (e.g., abstract algebra, topology, complex analysis), and it's not uncommon to have taken more than two grad courses, sometimes many more and in a few cases starting in high school.  Plus it's common to have undergraduate research experience or other substantial independent work, such as a senior thesis.

Basically, imagine yourself in four years.  That's who you're going to be competing against for admission, the other extraordinary high school students who went to college and became even more knowledgeable and impressive.

If you could find a university that would admit you to graduate school now, you'd probably end up going to a second tier school, spending some time catching up on courses, and then writing a good thesis but not living up to your potential.  Your career would get off to an inauspicious start, you'd have trouble on the job market, and in the long term you'd likely end up with a less research-oriented job than you might have had otherwise.

Of course I could be wrong about this: you might have exceptional luck or be the next Terry Tao.  But diving into graduate school at a young age with minimal preparation is an incredibly risky strategy.

This is something that's really hard to discern from college catalogs.  They usually focus on the minimal requirements to complete each degree and move on to the next level, but that's not how people do things in practice.  Instead, the vast majority of future mathematicians spend at least three years on their undergraduate studies, and generally four (in the U.S.).  The operative question isn't how quickly you can complete the degree requirements, but rather how much you can achieve along the way.  Preparing well for grad school is far more demanding than completing an undergraduate degree.

So what I'd recommend is that you pick an undergraduate program in which you'll have really outstanding fellow students, so that you learn from and are pushed by them.  Being part of a cohort like this is probably the single biggest factor in success, and your goal should be to find amazing people to hang around with and discuss mathematics.  You should then take whatever undergraduate courses are needed to fix up your background (if any) and move on to graduate courses.  You should also look for research opportunities during the summer or perhaps the school year, but it's not worth obsessing over this.  No program will guarantee anything, but at the very least you'll surely have some success applying to summer REUs, and it's reasonable to hope for even more than that.  Perhaps you'll finish in three years, and perhaps you'll decide to stay for four, but either way you'll be far better prepared for graduate school than you are now.

It sounds like you're in a great position to do well, with a remarkably strong mathematics background.  However, I'm convinced that the right question is how to get as much as possible from your undergraduate studies, rather than how to skip by them as quickly as you can.