If 3-3-1 gate hadn't happened, the judges scores/dance off decisions would have succeeded in getting rid of the three favourites with the public - I'm including JS here even though he didn't actually get to a dance off - and left the Beeb with a boring 2 couple final between the two people less popular with the public. I wonder how many votes there would have been then. As it was the public had to keep voting to get their choice over the judges. In fact if the judges had given Tom first place marks, there may have been less votes cast, the Tom fans would have been less desperate to save him. It's a coincidence of circumstances. I'm putting it no higher than that.
If anything needs changing it's not some formula to get rid of someone who is at the bottom of the judges table 3 weeks in a row, as has been suggested after JS departure, but how to get the balance back with the public. There is never a dance off in a 3 couple final, so there should not be one in the semi if a couple's resignation means the 3 down to 2 bit happens in the semi. 3-3-1 gate wouldn't have happened then, even on those marks, Tom would have gone through.
Personally I think there should be no dance off where there are 4 competing - either the dance off has done it's job by then, or if the public are that determined, let them have their choice, even if it's an amiable and entertaining non dancer like JS. I think that if the judges had made less fuss, the GBP would have had enough of the joke, especially if it meant losing Austin or Tom, once the difference in performance became more obvious.
If the audience is seen to have the power it should have, 'fix' allegations will become less relevant. People may still think the judges overmark, but GBP would have the power to override, so it wouldn't matter so much.