I think this is a smart and economical way to do it.
I knew I would be using MUS with future dc, so I went ahead and bought Alpha all the way through Epsilon (not all at one time though). I just fast tracked her through Alpha and Beta, and slowed down some in Gamma. She was about 10-11yo when we did this.
I think it is important for them to see how Steve does things right from the beginning. It almost always makes more sense than what we were taught growing up. I had so many "aha" moments, and I was good at math in school! The shortcuts and tricks he uses help so much. Some of them I figured out on my own, but only through looking at a lot of right answers and just kind of figuring out how it worked.
I think you an continue to work on math facts on the side. Not what Steve recommends but I think it can get discouraging to hold a child back for too long because of math facts. Just MHO :)