始めている (Beginning) and 進んでいる (Progressing) looks same to me, but not sure since you mentioned it.
I can confirm the rogue goes to the brothel with 始めている in the text, but goes to the slave market in the 進んでいる stage.
The adventurer though, not sure if she is bugged but she only has the 始めている text and disappears from the game if rescued in that stage.