I’m not reading throguh all of that.
So the simply answer is…
Number all the coins 1-12 and put them into groups of three.
Now weigh coins 1-3 against 4-6. If same weight move on to weighing 2 if not move onto weighing 3.
Weigh coins 7-9 against 10-12. One of these sets of 3 coins will be lighter.
Now take the three sets of coins that are in the group that are lighter and pick two of them. Weigh them against each other. If there are the same weight then the unweighed coin is the light one.
Volia. hehehehe. I like these things. More I say more.