Yes, there is lots of inconsistency in how this rule is applied by officials around our state, and around the nation. That is primarily because of the setup of officiating associations - they are literally independent bodies loosely organized under umbrella organizations like the WOA or the NFHS. It is frustrating for coaches and for referees as well - there are "regional variances" in how things work, when there don't need to be such differences. This is something which motivates me in participating in national forums, and in conducting statewide training here in Washington. But, let's move beyond this broader issue to the specific incident at hand.
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What should that coach have done differently? I can propose what I would have done, and I am a longtime wrestling referee, so I have a very deep knowledge of the rules and can choose my language very carefully. I coached for 5 years and only took a referee to the table 1 time - I could have done it many more times, but, sometimes as coaches, we have to accept that there will be certain calls which cannot be reversed. That being said, here is what I would have done if I was that coach:
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First thing is to insist on having my Coach Conference. In the replay, the way the "conference" went down looked too informal for my tastes and did not appear to give a full explanation of the rules dispute and the rationale for the call. I want to make sure that both parties know the conference has begun, and when it is finished.
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Secondly, when I have a conference, whether as a coach or as a referee, what is most effective is to use rules-based language and to focus on observable items/facts/data. The conference should always start with the coach raising the rule they believe was misapplied. In this situation, it would be the takedown award, but more specifically, the awarding of Control which is a requirement for fulfilling the takedown rule (Rule 5-25: control, down on the mat, inbounds, beyond reaction time OR feet finish inbounds). What is at question is whether the wrestler had control in order to then be awarded that final takedown. So I would have asked the official, "What constituted control when you awarded the takedown?". Then let the referee tell you what they saw, and what they were thinking, when they applied the rule for Control, and then the rule for Takedown.
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Third, After hearing what the referee observed and their rationale, you now have the ability to determine whether the rule may have been misapplied. In this situation at hand, the key issue was the position of the attacking wrestler's right leg/foot - it was not "laced" over the opponent's left leg, instead, it was resting on the right hip of the opponent. So, when the attacking wrestler is seeming to apply a Merkel hold, it isn't really a Merkel anyway. But, it's not the name of the move which determines control, it is always the two fundamental pieces from the Control Rule 5-6: Restraining Power + Position of Advantage. Based on what the referee recounts during the conference dictates how far you can go with the dispute. If the referee says they saw the legs interlaced, then you are kind of stuck because now we are in the realms of the "facts" or "observable" - and you are at an impasse if the referee tells you that they saw something you didn't see.
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Fourth, since it is a State Quarterfinal match, you push as hard as possible. The outcome of this match could literally be life-changing for the wrestlers, so you do whatever you can to seek justice. Like you said, the goal is to get it right for the KIDS, not for the adults so much. If the referee didn't see the leg on the hip, I would push that point - and insist that the leg was on the hip, not interlaced. Allow the referee to reconsider, "Did I actually see it with my eyes, or was I assuming the legs were interlaced????" Perhaps the referee might conclude, "Hey, I didn't actually look at the attacking wrestler's right leg", so it opens up the possibility to pursue the dispute further. Because if we get to that point, then my next question would be, "Would you consider it a position of advantage if that leg was resting on the opponent's hip?". The answer to that question is telling - because that is the core point of contention.
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Fifth, if the conference doesn't yield the desired result, then the coach should just insist on a protest and that the Games Committee convene at this mat. The mat should be shut down until the protest is concluded. The coach should remain, and I would keep my wrestler in the mat area as well, in case the remedy requires re-wrestling. I want my kid ready to go, and fully engaged, regardless of how this turns out.
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The protest is as far as a coach can take it. Sort of like having your "day in court" - if it doesn't turn out the way you wish, you have to accept it and move on. However, by keeping everything centered on the language straight out of the rules book, and establishing the facts/data/observations from the referee, that gives you the best chance possible to get things changed.
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Not sure that is a satisfying answer, but, it is the best I can propose in that type of situation.