There has to have been an infraction. What was the infraction?
More specifically, for an adjustment under Law 16: there has to have been UI, it must be the case that the UI could demonstrably have suggested the call chosen, there must be a logical alternative call that leads to a better result for the NOS.
The "broad license" to which you refer, Peachy, is currently Law 12A1:
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The director may award an adjusted score when he judges that these Laws do not provide indemnity to a non-offending contestant for the particular type of violation committed by an opponent.
If the violation was "use of UI", and Law 16 does not lead to a score adjustment, you cannot, IMO, use this law to adjust the score (this may be a change in approach from your "years ago", I don't know). There is also Law 12B2:
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The director may not award an adjusted score on the ground that the rectification provided in these Laws is either unduly severe or advantageous to either side.
Edgar Kaplan is said to have been of the opinion that the TD should decide what ruling he wants to make, and then look for a law to support it. That approach is no longer favored - instead the TD should do his best to make the correct legal ruling, even if in his opinion that ruling isn't "enough".
There is this, wrt to your 1S-3S-6S case: Law 73C says
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When a player has available to him unauthorized information from his partner, such as from a remark, question, explanation, gesture, mannerism, undue emphasis, inflection, haste or hesitation, an unexpected alert or failure to alert, he must carefully avoid taking any advantage from that unauthorized information.
But there is no score adjustment from this, because the criteria for score adjustment in case of violation of this law are in Law 73F, and that law does not apply to this situation. I suppose that a TD could rule that the frustrated player violated Law 73C, and then invoke 12A1 to justify a score adjustment. OTOH, we had a discussion here not too long ago about whether you can do this if 16 doesn't lead to an adjustment anyway. There were various opinions; I'm not sure we came to a conclusion.
Whatever the TD decides to do though, he has to be able to show that there was an infraction, and that the law tells him to adjust the score because of that infraction. In the instant case (passing 4NT), I don't see any such justification.