I don't think you, Dr. Harley, my wife and I are in any disagreement about biblical submission.
the "problem" is in the application.
First off..."biblical counselling" isn't the ACTUAL bible doing the counselling. It's a man or woman of faith (minister, preacher, whatever) that may have a little to no training under their belt. They very likely have little to no understanding of the wayward mindset. They also may or may not agree with OUR understanding of biblical submission. The counsellor/minister is not God himself, obviously, and is just utilizing a counselling program designed by a man (Jay Adams) based upon scripture. As such...there is nothing stopping such counseller/minister to belivers utilizing the MB plans AND talking about the trilogy of Husband - Wife - God and even explaining "submission" in the context you described above and as it relates to POJA. Maybe Dr. Harley should write the same plan and put in the word "God" 50 times and THAT would make it biblical?????? Just because non-believers can use MB successfully doesn't mean believers can't also use it as a biblical counselling program with Him involved as the "ultimate authority".
Second...the Believer (not talking to or about non-believers) audience, particularly the wayward spouse (trying or not to become a former wayward spouse) is about as far away from God as one can get as a Believer. HE/SHE won't likely be responsive to the word "submission" in any way shape or form right from the get-go. A betrayed wife isn't going to be thrilled with "submitting" (in the misunderstood common knowledge sense of the word) nor is the wayward wife at all ready to "submit" at all. You and I have both been there with WW's and invoking the name of God was definitely a "don't" in our household AT THAT TIME. Waywards are repulsed by such...unfortunately. MB in it's secularishness (lol) is, perhaps, a great way to sneak a biblical counselling program in the back door.
I do like Nouthetic counsellings notions of confrontation of sin.
I'm not a fan of it's outright dismissal of all things science (or, more particularly) the mental sciences. Science was once fully the pursuit of His laws. I'm not a fan of conventionaly non-directional counselling/naval-gazing, but ignoring EVERYTHING He has revealled to us in the entire field of pyschology is a mistake.
I haven't seen statistics about it's success but GUESS that it's likely much less successful than MB for recovering marriages in the early stages of infidelity....if you can even get a wayward spouse there.
That being said, Nouthetic counselling, in my opinion, MAY be a good adjunct to MB principles for Believers (obviously) after one or two years of actual recovery utilizing the scientifically proven MB methods to get the recovery off the ground FIRST with the practices Dr. Harley has observed in wonderful marriages. The "rules" of MB are both "Golden" AND Scriptural...thus, equally applicable by conventional (directional) counsellors and biblical counsellors alike. There's certainly no harm in putting off Nouthetic Counselling and applying MB FIRST and continuing MB while then Nouthetic Counselling. In fact...Believers may want to look for a counsellor/minister/preacher that's familiar and likes/applies BOTH programs.
Course that's just my opinion and understanding TODAY....that and a dollar will buy you a cup of coffee.