1. You have already concluded that the exact hands/board cannot be reconstructed, so we will concede that point.
2. Next I would go to TDA Rule 10, to see if a majority of the players, whether in the hand or not, agree the pot was awarded incorrectly and, if so, to which player the pot should be awarded.
3. Note that I did not say in #2 if the players agreed on the construction of the winning hand.
4. If I did not get a majority in step 2, then I would have to weigh what the players who said there was a different winning hand against those that a) were not paying attention, and/or b) those that don't agree there was a different winning hand. If there were more players who agreed to whom the pot should be awarded than there were those against, I would rule the pot goes to the tabled winning hand even though the hand could not be reconstructed.
If the alleged winning hand cannot be identified and if the players cannot agree the pot was awarded incorrectly, then I submit the pot has to stand as awarded. In order to make the change, you have to have some level of evidence/confidence not only that an error was made, but what the correct decision should be.
Remember, in most small tournaments, whether in poker leagues, bars or whatever, it is highly UNLIKELY there are any cameras to record the action anyway.
Hope this helps!!