My understanding is that in a plurality decision a majority of the judges agrees on what the final outcome should be, but not why. So they may write separate opinions as to why they agree with the result but explain their different reasons why they think that should be the result. (There may also be dissenting opinions, but those are not part of the plurality.) No single rationale commands a majority of the judges, so this is why it is not a majority decision. The statement "the controlling precedent is determined by the opinion that concurred in the judgment on the narrowest grounds" is new to me but seems to be correct. For example, a judge who thinks the case should be decided on some procedural technicality would be stating a "narrower ground" than one who thinks it should be decided on some evidential issue.
With a three-member disciplinaty panel, a plurality decision would require at least two of you to agree what the result should be (e.g., suspend the member for 30 days) but not necessarily why. Since you aren't concerned with the precedential value or "narrowest ground" of your decision, you don't have the same concerns as a court. Perhaps your club rules don't even require you to explain your reasoning - just issue a decision. If they require a unanimous decision, then three votes for the same result would satisfy that even though all three members had different reasoning. If they simply require a majority vote, then two votes would satisfy that even though the two members disagree on the reasoning. If the three panel members voted for exoneration, a 30-day suspension and a 60-day suspension, you'd have nothing and would have to hash it out.