Padres are already an invaluable resource for mental health. I'm not remotely religious, but found having a padre to talk to at times was a real help and comfort. They're there for pastoral care and to listen, and often seemed to be more attuned to things than a 'professional' therapist. Effectively I found the padres to be exactly what you're suggesting!
Not sure what they could be replaced by that would provide more benefit. More CPNs would be sat on an appointment-only basis at the med centre. The current setup, whereby you can access a bit of help through a padre who can work wonders to get you in front of the correct MH professional seems good to me.