Thinking about key points in positioning a room, I decided doors were a good idea, so I tried to code up a routine that would reasonably place doors. I interpolated about 30% up along a line and placed a small black perpendicular line prependicular to the line along the centre of the corridor. I went with the simple rule of thumb that a point that connected more than two corridors was the centre of the room. I got this:
Not bad, but not quite right. Probably the best way forward is to decide on an overall radius that will establish the size of the room and fit the doors to that.