A couple ideas to tweak this to k-12, at least baby steps for more traditional teachers.
1- have students re-write math word problems by changing the characters and events, but keep the math. Students don't have to re-write, but most do, and they really get into it, and bring in their own culture and I get to know them.
2 -I give students a 3x3 grid with different outputs for students to show mastery. Examples include having students: make a quiz, take a quiz, make a video, write an essay, find real world application/primary sources. I arrange the tasks in the 3x3 grid so students get experience in different levels of technology and grouping. This is a gateway to the student agency you're describing.
This is a great idea. I want to steal it for working with the teachers I coach. Specifically I have 40 teacher colleagues all working on Ed tech integration, this is a great way to get professionals sharing and supporting