I am rather confused about your experience with the 'High Level Complaints' team, as I know fine well what a brilliant job they do.
When a HLC is raised, their team contact the operations manager for the area in question and he/she have to nominate the best person for the task .... most engineers are multi-skilled, but some will have greater knowledge in a particular skill-set.
When the engineer receives the task, they will also receive an accompanying e-mail with a full historical breakdown of the issue, including all notes from previous engineers and the ISP.
Once the info has been read, they then have to make contact with the HLC team by way of a phone call to ensure they have understood what the issue is and the result that is expected of them.
At the end of the task, they have to have another phone call with the HLC team who scrutinise any and all test results performed and have an in-depth conversation about the engineers findings. Only when they are happy that the issue has been fully resolved, or we have gone as far as we can within our remit ... will they close the case down.
Having done many of the HLC's myself, I can assure you their department really aren't intransigent. The polar opposite, in fact.
I may get time to have a look-see later on, if you can give me your DP number ??. No other info please, simply your Exchange and DP.