This article may help you some–it’s about fitting any curriculum into the Math Daily 3 structure.
https://www.thedailycafe.com/articles/Using-the-Math-Daily-3-Structure-with-your-Curriculum

I will also be using EngageNY in 2nd grade. I am just starting with the CAFE webinar, then will do the Daily 5 and Daily 3 next month. However, in my pre-webinar thinking stage, I thought about having the fluency part of EngageNY be one of the parts where they are on their own for practice… I do like the chart they have on the link in their reply to you. That will help with breaking down I think.

Hi there! I am new to the Daily 3 and doing the online webinar this month. I teach 2nd grade and Engage NY was our new math program last year. It was really hard to get everything in with a new lesson each day. Looking into this upcoming year, I would love to hear any feedback on how you used, or might use, the Daily 3 with this intense program. I liked MCOY’s comment about using the fluency for the ‘work on your own’ part. But, I had quite a few non-readers or emerging readers, so I am not sure how that would/could work? Thank you for any comments or suggestions!