Cone ink refill bottles

I just got my new R3000 Cone carts and ink. When I do the first vacuum fill I'm supposed to draw ~40 ml from the bottle. But these bottles have a really small mouth:



Because the mouth is so small, the blunt needle fills it completely and air is trapped in the bottle so when trying to draw out the ink a vacuum inside the bottle is created, so you can't draw out 40 ml before it becomes impossible to overcome the vacuum. I don't run into this problem with my Inkjetcarts inks (wide mouth on the bottle).

Is there some other method to draw the ink out?