Would I be right in thinking that the OP has been knocked back when applying for airline jobs?
I would suggest that the ability to pass the ‘beer test’ is an important factor when selecting any crew member.
A sound selection process would be able to determine this key issue.
The comparision with a doctor would be a good bed side manner. Prospective UK medical students do undergo aptitude testing as part of the selection process. For a lawyer, empathy with the client.
The issue with the modular route is that as a ‘self improver’ chooses whether they are suitable, and has the ability to pay for the training. Perhaps taking a psychometric assessment such as 16PF would assist in identifying just what characteristics you process and to what extent your personality is suitable for multi crew flying.
Interviews will invariably include a flight crew member and not just HR. Although I take your point about the influence HR appear to have in hiring pilots.