The third way is the liberal way, just at a slower speed.
The “third way” has been standard progressive jargon for a century (and not just in religion, but politics in general), because they understand it is a way to achieve their goal. They may achieve it more slowly, but in the end, they win.
I agree with you that the third way is stealthy and all the more dangerous. Sort of how we got to this point in the general culture....in many areas.
The denominations mentioned are all considered "liberal." Not from a political standpoint, but theologically.
It all started in the mid 1800s when the inerranccy of Scripture was undermined. It was said then that Scripture is all about man's experience with God, not God's word to man. Paul hated women. On and on it went.
Since they gutted the supernatural, these denominations became more interested in being agents of Social change. Prohibition comes to mind. Women were made ministers. The line between right and wrong became increasingly blurred.
It should be no surprise that this is happening. Theologically conservative denominations will do fine. The old guard has become irrelevant.