Yeast slurry is a Non-Newtonian Fluid; if you want a good example think of very thick custard.
The cones of conical fermenters must be reasonably steep (60 o& 90o are both pretty common but mostly the first because its a circle cone thats easy to make and forms an equilateral triangle).
Commercially they are also polished to death, usually electro polished so the yeast slides off easier the home brew ones are just buffed nowhere near as smooth and nowhere near as good at shedding yeast.
If you put some custard in a funnel (put your finger over the end) then some water on top, remove the finger and the middle will fall out of the custard, then the water and a bits of custard mixed together will flow out, when the water is gone the last of the custard will gloop out in other words a real mess.
Try taping on the cone or the bottom tap with a bit of wood, this will help dethatch the yeast from the walls and have it fall into the cone, then remove the yeast in small portions (couple of hundred mills), maybe giving the cone a bit of a tap and a rest before drawing more.
Mark