I think it is very important to only use crowns on resources. The prices are much less. I am not a math ace, but I will try.
For example, to fill my storage with 5,954,630 gold costs 2,221 crowns. This means each crown is worth roughly 2681 gold.
I have 1 day, 12 hours left on my spike trap with one guy working (it might be 1 day, 12 hours, 59 minutes but it is impossible to know). It costs 376 crowns to finish instantly. This means an hour of reduced build time is worth 10.4 crowns.
So, this would mean that an hour of reduced time is worth 28,002 gold roughly.
It is important to note that the cost of speeding up appears to be strictly set. For example, 4 guys working on a Market with 36 hours left costs the same as one guy working on a spike trap with 36 hours left. Not four times as much.
To me, it's much easier to wait an hour than to lose 28K resources. So it's much more efficient to use the crowns only to pay for resources, never to speed up the projects.
Now, I have no idea about the costs for speeding up non-building things. Clearly, generals cost less than 10.4 crowns per hour and soldiers may cost more. I am also not sure about potions and research/blacksmith.
The most important takeaway is that when you see the "instant cost" most of that cost is likely to be for the time as opposed to the resources.
I hope that helps.