Welcome to Safe Speed concernedparent

I think you are trying to tackle a problem of psychology in driving.
Pent up frustration from the main roads and the lights to which you speak are at fault, by the sound of it. Solve the core problem and the 'effects' of that problem tend to go away.
Long 'on red' lights can cause untold frustration, so when a driver / road user then finds a little tarmac they can be a little excessive.
How can you tell they are going above the limit ?
Generally speaking drivers slow when they see a hazard, so can I assume (legally right or wrong put aside for the minute), that when you see these vehicles accused of going quicker, are they going too quickly for the conditions ?
Are there hoards of kids and so on about ? Or even any kids / people etc about ?
Is it that you 'fear' something may happen, because you have lost faith in anyone going over what might appear to be a posted limit?
Have you got the stats for the Aberdeen area residential roads ?
Some cars can 'look' a lot faster from the roadside than when you are in them, it can be deceptive.
I disagree with many road furnishings for many reasons, but they include car damage, and distraction.
We must ensure that drivers / road users understand their responsibilities to themselves and each other.
Instilling better practices in road users, to ensure they only go at speeds that are right for the conditions (one that they can stop int he distance that they can see to be clear in).
The VAS (Vehicle Activated Signs) are quite good at reminding people of their speed at that given location, and have been proven to guide drivers to act appropriately. This maybe worth suggesting to your local Council, to have a proper survey carried out. Talk to your local Police Station and see if an officer can visit and have a presence at the 'problem' times. I am sure that you help a lot. We are all for Traffic Police presence as it is proven that they are the best deterrent of all.
A proper Road Engineer needs to come down and survey the whole area, and understand why the rat-run has become necessary in the first place. Why is another route less favoured. Keeping good traffic flow onto the main roads ensures small roads do not take anything other than some overflow from time to time.
From the map it is not clear where or why they are using the roads you mention, and I assume the road parallel to you is also used ?
If they are 'on their way home' are they going N or S ? And if it is only a few cars then is it also in the morning too or just the evening ?