We are trying to debate acceleration of subjects vs depth in various subjects. But this is most glaring for us in math. For example for any level in math there is in order of depth:

1. School math
2. Basic level math core age from books
3. EPGY/Khan academy level math
4. AOPS level math
5. etc etc

How have you traded off on mastery of depth vs advancing in grade levels?

I've completely sacrificed depth for advancing so far. Why? Because I'm in a Common Core district, and the virtual school - our best option for many other reasons - does standards-based assessments.

However, we just did formal 3-grade skip today. So he has access to middle and high school classes which are more in depth on a single subject. Now I can flip to depth with no need for acclereation. (I hope! I tell myself!). LOL

It's pretty hard to get depth without acceleration in math in K-8?

For math, you need to make sure they have math facts (depth) down thoroughly well, or it will hold them up in later math classes. They need to know quickly and solidly addition, subtraction, etc. So early depth is super important, IMHO.
Later on, you can go for problem solving skills and advancing. The common core seems to repeat itself, so if you miss some concept one year, it will surface again later.
My son is taking a one year high school geometry class in 5 weeks. I'm helping him, although I don't remember a lot of this stuff! However, looking in his textbook and watching Khan Academy videos allowed me to figure out all of the questions and go over it with him. (Problem solving skills!)

Portia what is the material you use for science?

The short answer is mastery of depth over advancing in grade levels to the extent possible. The higher level your student attains the more obviously beneficial this approach will prove to be.

However, practically speaking, you have an additional obstacle due to the low level of your "School math". One possible solution is to disregard school math and proceed independently to ensure depth. If in fact your school math is so extremely low level, there is little benefit/meaning in advancing in grade levels unless you supplement with depth simultaneously.

In our case, school math is higher level than EPGY and significantly higher level than Khan Aacdemy. I am judging EPGY based on what I have seen of CTY(similar curriculum) and the fact that our district stopped allowing its use a few years ago as an alternative curriculum for certain accelerated (beyond regular GT) students who needed an online course. It appears not to have kept up with advances over the last decade so that there are holes in areas such as word problems, problem solving and written explanations compared to what our GT students are supposed to master. Khan Academy is very basic coverage meant for the "Everyman" rather than GT students. It is great for basic practice, remediation and an additional source of quick topic coverage.

If your child is to keep pace with high achieving students nationally, you need to go beyond Khan Academy level math. AOPS is an obvious choice for Pre-Algebra and beyond. I am not familiar with Beast Academy but presumes it has depth due to the source. Glenn Ellison (an MIT Economics professor who coached mathcounts) also has a book aimed at middle school competition level math and another one aimed at elementary kids. DS used the middle school one the summer after 4th grade (after completing school GT Pre-Algebra) and learned some new topics. I considered the elementary one for DD and he kindly PM me to offer a few chapters via email after we exchanged posts on this forum.

Sometimes you do need to double back, particularly for higher level math courses. The AOPS courses are invaluable for the proof writing and challenge problems. If you can't takes the courses, the books will provide some challenge although not as much as the actual courses.

For those of you using AOPS, what is the time commitment? Realizing DS needs something more but concerned about fitting it in after school hours.

I think AoPS says to expect about six hours a week, including the hour and a half of class time. DD12 did more than that for the first couple of weeks of Algebra, but it has settled down to that or a little less. When she took Beginning Python, it was considerably less - probably more like three hours a week.

Time required for AoPS depends a lot on how many of the problems you need/ choose to do. If you already know a lot of the material and just want to add depth, you can jump ahead to the course homework and challenge problems; 3-6 hours per chapter (Algebra was usually about a chapter per week) might do it. However, if you are learning new concepts and need to work through the regular problems in each section, as well as those at the end of the chapter, and then do the chapter's challenge problems, and also do the assigned Alcumus problems, plus that week's homework assignment... it could take much longer. The whole point of AoPS is to throw problems at you that you need to spend a lot of time thinking about, so it does that job best when you allow yourself enough time to think, and to try all the problems.

ETA: which is why we switched from on-line course to self-paced home study with Mom - we just needed more flexibility in the after-schooling schedule

I think I read somewhere on the site (from AOPS people) an estimate of 5-7 hours (including class time) for the courses in the introductory series. The actual time can vary depending on whether the student is okay with half green, wants all blue, or wants beyond all blue (i.e., get every single challenge problem). I believe you can get an "A" for a transcript with mostly (at least a lot of) greens. It is possible to get blue on the challenge problems category with a couple of problems undone if the completed ones were correct on the first try so that you were awarded the maximum 7 points rather than 5 or 3 or 1 after additional attempts. It doesn't take much time to achieve green, more time to earn blue and potentially a lot more time to get every problem correct. Sometimes DS can get every single problem well with that 5-7 hour window but there have been some weeks where DS spent 8-10 hours with 2- 4 of those hours spent on the last 1 or 2 problems. For DS, this was sometimes an issue with the Geometry course while in the Algebra 2 course he could almost always complete within or even below the estimated time.