Hi Lisha - good to hear from you. I can't really work out what method the individual is using. By converse return, I interpret this as the converse solar return for the birthday (Sun returning to the degree and minute that is at at birth). The time and date I get for this is 5/9/1966 at 14:07 for the birthplace giving 25 Sag 51 rising. I'm afraid I can't recreate the chart details set out below by the person born 4/9/1984 for any return chart. The closest I can get is the straight converse return for 5/9/1966 at the birthtime, but whilst Moon and Neptune are opposite, conjunct the nodal axis, Venus isn't rising.
If you are calculating for the converse lunar return, I get the same chart as you have posted above. I think there is a lot in your method as the chart seems very apt.
Thanks for the update. Ed