Thank you for your question. We had actually answered this question in the live session. I really appreciate that you have in the effort to apply the method in real life and that too with a team! Thank you for sharing that with us.
Short summary - don't get too hung up on process alone, but focus on what we are trying to achieve. We want to get an understanding of the root cause of the problem. An unsaid need is what we are looking for. If one of the branches has lead us there, so be it. Let's pick that up and then run the conflict of interest analysis on that one particular one.
Main reason we do these analyses (which are not prescribed in detail by the Stanford or the Ideo method, it is indeed prescribed by Prof. Karl Ulrich of U Pennsylvania), is to understand the unsaid need. 5-whys and conflict of interest is one way of doing it.
I hope this answers your query.