Digging into a mountain?

So I'm playing my first real game after trying it for a bit around the Steam release and so far so good, but one thing drives me up the wall.

I'm going for a Human/Cretonian/Dandorian city so for the third of my pop and majority of my industry I want to be in the mountain, but it takes fucking forever.

Looks like I need tools for hospitals, so for the last 2 hours of gameplay I'm borderline idling around 900 pops waiting for my 60 to 80 oddjobbers to get to the bloody coal and iron veins. And they aren't even that far!

What am I missing here? Is there a way for this not to take that long? Surely I'm doing something wrong here. Here's the screenshot of my town with those (now almost finished) mine shafts.