There is a very simple reason why your second example is not correct: English does not use the perfect tense forms of the progressive aspect of the passive voice.
We just do not say ‘has/had been being done’.
You can say ‘has/had been done’ (perfect passive) or ‘is/was being done’ (progressive passive), but not ‘has/had been being done’ (perfect progressive passive). You choose either perfect tense or progressive aspect in the passive, but not both at once.
Therefore, in your case, you can choose either the perfect passive:
Procedure that had no longer been followed
– or the progressive passive:
Procedure that was no longer being followed
In this case, the progressive aspect of the non-following is more important than the perfective aspect, therefore the progressive form ‘wins’ and is more natural-sounding.
Your way of considering the perfect construction and its semantic meaning is correct, and if the verb had been in the active mood, the past perfect progressive would indeed have been the proper form to use:
I was able to reintroduce the procedure, which we had no longer been following (up to that point).