I'm working on my own basement slowly and have decided in the end to go a different route.
I installed cork over my basement slab. 1/4" stock and I set it with Laticrete 254. After leaving this and working on and walking on it for months the cork is stuck amazingly well and I'm even thinking I do not need heat anymore. The cork by itself has taken the entire chill out of my mudroom.
Grani Rapid from Mapei and many of the highly modified thin sets bite really well to styrofoam. I would consider using this in tandom with your design to ensure you have the styrofoam installed tight to the slab. Perhaps install a sheet at a time and use wedge pins and plywood to "Clamp" the styrofoam while the thinset sets up.
You do not want a moisture sandwich so if you choose the Ditr route do not band the seams.
There is a lot of confusion and conflicting advice in this project of yours.
Good luck with your research. You will find like me I'm sure your in for a head ache of duelling advice.