Hi Well the good news is that we don't have a tight deadline until they sell the property or something similar You clearly understand most of the process - and it is marginally easier to challenge the calculations - once you have them - under the new(er) rules. I have to be honest from what you said about the appeal it was doomed to failure from the beginning as none of the grounds that you speak of represent an actual answer to the assessment.
Of course that does not explain the incredible hike in the arrears but a freedom of information request relating to the calculations should assist and allow you to challenge the figure
This group http://www.nacsa.co.uk/ is likely to be able to support you in this.
I hope that this is of assistance