** snip **
>After the block was in place, each
> time we even looked at a page, the block was automatically extended,
> which made it appear to other admins that we were acting in bad faith,
> trying to made edits while blocked.
An edit attempt after one has been blocked should not be considered acting in bad faith, because often that is the only way one finds out that one has been blocked. I received no notice on my talk page for instance. Someone may not attempt an edit for hours, so the current automation (which has been admitted to be erroneous) would add those hours to the 24 hour period. Attempting and edit might also be a legitimate way to check if the block is over.
Unfortunately, the current system blocks the usual wiki ways to communicate on talk pages, and does not automatically unblock you, that requires an error prone and burdensome manual vigilance on the part of the administrators. The good news is that they are aware of this and asking for a solution.
-- Silverback