Caveat: I did some education pro-bono work while at MBB, have been Strategy Committee Chair at a non-profit for the past few years, but all my interviews were "economics focused" as you put it.
1. McK, like Bain and BCG obviously, does a lot of work in the non-profit sector. One of the things we bring to these sectors in a professional/profit-focused angle to help them become more efficient & effective
2. Most interview cases are probably 'economics' focused indeed, just like most actual projects are. They don't make for cool stories necessarily, so consultants are likely to tell you about that one time they did something "different" instead. Don't fall for this sampling biais.
3. Applicants put too much focus on doing cases from a specific industry vs. learning to understand and crack cases in general. Once you know how to do a case in a repeatable, structured and MECE way, you will know how to do the next case no matter the industry
4. I bet all of us here have a few non-profit/education cases available, even if they are not our go-tos. If that's really what you want, we can give such cases to you. Again though, I highly suggest you focus on the mechanics of the case first, second and third
5.. Your last question, with 1st round more 'economics' and 2nd round more 'experimental', probably has a kernal of truth: 1st round interviews are led by Consultants and EMs, while 2nd round are led by Partners or APs who may not feel as constrained by the general guidelines, and want to test your creativity and personality a little more
Hope this helps; let me know if you have more questions on the above.