FWIW, Singapore Math recently released an online curriculum for Primary 1-5, which might be useful as a counteroffer.
https://www.singaporemath.com/SearchResults.asp?Cat=291It has built-in mini-lessons, pre/post-tests, and intervention assessments that can be auto-scored and used for identifying gaps for intervention, which might be some ways you could document the presence/absence of gaps, where they are, and which aspects of SM would be relevant to teach for the purposes of gap-filling. I know the "system" might still be an issue for you (though I've found it to be generally quite intuitive for my particular math-y kids), but it would at least allow you a means of accelerating/compacting through a curriculum that the school cannot object to. SM also has semester-level placement tests (essentially end-of-semester tests), for which they suggest 80% is mastery.
