Yep, Engineering do it.
As you mentioned, in other airlines, the engineers get a ~monthly workpack from planning to check/update the figures for IDLE/PERF. There is an AMM task for exactly this - it's a 2 minute job. (We used to have a sheet that had IDLE/PERF figures for every aircraft in our fleet, in a previous life).
Sadly, the issue you seem to have is everyone in Part M is washing their hands of the responsibility for the IDLE factor. The FCOM states +4 is the default (if it has never been changed) - and this is what it is set to.
As you know, the fleet are set at 0 due to the aerodynamic differences, which is the correct value to use.
So it remains set at +4, the default value because nobody will confirm that 0 is indeed the correct value for that airframe. I suspect the others were set at delivery.
All that needs to happen is the 'Airline', Part M/Ops need to produce a sheet of figures. Then this should be distributed by Planning down the the Part 145 engineers in a workpack for them to update the figures. It's simple, shame about the politics involved!