we tried "Saxon math", Singapore math dimensions, and Beast Academy.

And my impression was that Saxon Math was the worst. What I mean by worst is that it just make you practice an algorithm by doing lot of repetition but doesn't force you to have a deep understanding or problem solving skill.

Saxon math worked out for me, although we didn’t shop around as far as I remember, so maybe Singapore would have worked fine as well.

My experience is that I didn’t really feel like I was memorizing an algorithm. Because the problem set includes assignments from all of the old sets, it is hard to memorize all of the algorithms. So you instead memorize the different moves that are allowed and have a general idea of what types of moves might be useful.

I dunno. I went on to do engineery stuff as an undergrad rather than pure math stuff, it seems like a good match because engineering problems are also often in the “no need to be super clever, just don’t mess up” vein, so it could be just a lucky match. This is what I mean by muscle memory — I’ll use the famous names theorems when necessary but sometimes you just need to bash the math until the thing you want is on that side of the equal sign and the other stuff is on the other side.

I think anything that results in

1) actually reading some textbook

2) actually working through problems for a couple hours a week

will compare well to the typical US math education pretty well anyway.