That CFI must have had chapter and verse on the W&B limitations of a PA28 140; anyone who has owned one knows that 4 adults plus fuel - even to tabs (128l therefore 3hrs flying time, plus diversion) - will result in an aircraft which is out of W&B and CofG by quite some margin. You don't need to work the detailed calculations - you know that it won't work - period.
Whatever the reasons, that flight should not have taken off for three reasons that were well known to the CFI;
1. W&B
2. Currency
3. The aircraft was not equipped for the prevailing IMC conditions
Apart from point 3 everything else you have pointed out is irrelevant. The accident occurred on the flight home which was inside W&B. Currency, well the outbound flight would have covered currency if not legality with regards to the number of take of and landing.
The final point is the valid one, the aircraft was not equipped for IMC conditions yet the crew chose to take off and fly back knowing the conditions. They chose not to divert at anytime on the return despite having a number of FULLY VFR options to choose from.
I agree with vanHorck, I can't see any outside factors that applied to the accident flight other than crew error as a result of pushing on when a correct command decision would have been to divert.
But as I have said, I am open minded and happy to see direct evidence that that the crew were coerced into the flight to such a level that they were prepared to risk and ultimately pay with their lives.