A recent Atlantic article [1] by someone involved in the Mississippi reforms gives a good outline of what they did/are doing. It includes science-based reading curriculum and holding kids back (as you mentioned). It also includes other forms of accountability, including parental notification and empowering the state to force recalcitrant districts to improve. One notable quote:

"The law allowed the state to abolish these districts’ local school board and remove the local superintendent in favor of a state appointee who would report directly to the state board of education. A later amendment provided that removed local-school-board members would be barred from serving in that capacity again."

Politically unpopular in some cases (which local jurisdiction wants the state coming in and replacing your local school board?), but seems to be pretty effective.

[1] https://www.theatlantic.com/ideas/2026/04/mississippi-educat... (gift link)