I've done this with a Blur LTC and it raises things more than you think. The increased a to c for an equivalent 27.5 fork (same travel) is about 10mm. The 27.5 wheel will raise things another ~12mm. Plus you're going with 10mm more travel. That's like adding 32mm. Much like running a 172mm 26" fork/wheel. It's a lot, but since you're running the bike as a park/shuttle bike it might be fun. Can you get a fork you can lower 10mm if you think it's too high?
I was planning to just use the 26in wheel. I figured the front end was going to be about 20mm higher. 140mm to 150mm and an extra 10mm with the longer axle to crown of the 27.5 fork. I used the Mach 5 at Summit a lot this summer. Just looking for a slight rise in the front.