Story Weaver:
But on the game style itself...
It is potentially interesting, but I might think to ask you, are you looking at it all with DW tinted goggles?
I forget the appropriate one, but if it is purely story, with only rolls for the unsure feeling things, then maybe another system might have what we need?
Mmm, no, hope not... Don't really want to examine another system...
Story Weaver:
Also, how would you codify "turns" in this manner anyway?
You just write until you want to give it to the other person... Which in dialogue between characters on my side and one your side (that is, character one of us controls talking to a character the other one controls, and vice-versa, plural when applicable) could be pretty quick turnaround...
Would it be useful if I told you about the setting I have in mind, or not yet?