Based on my experience, I can tell you that the initial and best form of training your tolerance to pain has to come from an external source rather than self-reliance. In other words, someone other than you pushing you through a pain barrier would be the way to go, if you truly wish to experience a level that is close to your true physiological pain threshold.
I have been pushed to a point where I had fainted for a brief moment (whilst going through an Olympic weightlifting circuit).This is not a state you can reach on your own I believe. I'm not suggesting you go through some pain barrier until you faint, but this experience I'm sharing here is simply to illustrate that "to break through a conservative pain barrier so that you can operate closer to a true physiological limit,” in my opinion requires an external source, at least initially until you know how it feels and how far you can truly take it, and how much you've been holding back during a set of muscular pain or whatever it is that you thought was going to destroy you if you were to continue on with it.