If you don't need the fade part, use BlackScreen then ActionStartConversation without delay. As others have observed, once the screen is black, any new conversation window appears on that black screen.
Regarding on-screen conversation with floating text, there's also SpeakString, if that makes a difference. You can manage the timing and presentation more easily using the
Gestalt dialogue functions (available
here).
Personally, I try to avoid floating text, as the conversation window gives the player more control to suit their own reading speed, but I can see that's tricky when the speakers are moving. You'd have to have the conversation owner moving with the group, so that no speaker ever moves out of range, and allow for the possibility that the walkers reach the end of the walk before the player has read all the lines.
