I did a similar tile in my entryway this fall. It is along an outside wall, but it receives a lot of traffic and the floor joists run along it's length, not across. I cross braced underneath and I used 1/8th Hardibacker. I also used very tight grout joints. In the pic it looks like grey, but the grout was darn near black.
So far, so good. No cracking or creaking. I did it myself in two days. The key for me was to lay the whole tiles, rent a wet saw, and then cut lay the rest. I also did a large kitchen in my old home with slate pretty much the same way. Never a problem.
