So I've mined the two mines, both extracted etc, and Mantid is still getting pissy with me after the 4 cycles are up.

I've collected all the colour from Pharynx after letting it sit a cycle, but I don't have time to do so for Bastion. The veins are extracted, but I'm having to wait a cycle for the colour to come into them. Question being, does the game only recognise completion of the quest after I've picked up the results?

Yes. All exposed and extracted areas have to be completely drained of colour. I had a similar problem - it turned out I'd missed one drop of Amber in Pharynx.