Yes, you are right about Montessoris in that you must complete every single item before moving on. It can be very tedious. The child is not allowed to skip things they already know.
For math, we mix and match- we did IXL when the kids were really little; Montessori PreK-first; Singapore Math, and now some other things. My third grader is breezing through a 5th grade math book- I'm happy with that for now.
Our school doesn't do alot of math competitions, which is a bummer; you can't really do that until junior high here. I'm buying a MOEMs book and will just try to work some of the problems with my kids.
Both of my kids are 2 grade levels above where they are in school for math and reading, and that seems good for now. Our school district doesn't skip anyone since we have an excellent full-time G/T program starting in 4th grade. Both kids seem very happy and have lots of friends, etc.
I figure they will have lots and lots of G/T opportunities in high school (over 30 AP courses), they can get into molecular research in nearby labs and try for the Intel Competition, etc. Maybe you can just keep trying to plug the academic holes at home that the school leaves behind.