This is all getting unnecessarily complicated.
I've seen a post on here before that suggests using percentage scores rather than finishing positions on the judges leaderboard. This would make all parties happy. There would be plenty of chance for people to overcome poor scores provided they had enough public support. As the competition goes on though, the deficit to the better dancers would increase based on judges scores requiring a much greater public support to keep them in.
I'll illustrate with an example (because I'm bored and have nothing to do)
Contestant A - lets call him Quentin Widdecombe, gets a score of 10 from the judges.
8 other contestants score 20 and contestant B, lets call her Kara Halfpenny gets 30.
The 10 dancers score total 200 and each contestants scores are calculated as a percentage of that total. The 8 dancers with a score of 20 would each get 10% of the vote with Quentin getting 5% and Kara getting 15%.
Quentin would then only need to get 5% more vote than the least supported of the 8 middling dancers to stay in.
When it gets to the final 4 dancers though it becomes trickier for Quentin to get through. Assuming Quentin hadn't improved much and got a 15 from the judges with 2 other contestants with 25 and Kara getting 35. The total for all scores would be 100.
Quentin would need now need an extra 10% of the judges vote to stay in above the middling dancers. 20% more than Kara!
I would have thought this would appeal to the BBC as well as people supporting weaker dancers would realise the need to vote plenty to keep in their particular homunculous.
Disclaimer - the charcters mentioned above are pure fiction and are in no way meant to depict characters real or otherwise.