The pick up tube sucks from the bottom of the tank regardless if the fuel is low or high. So if this is gunk it must be floating gunk! But you said if you prime it then the engine starts to run fine again. So it is not about the pick up tube getting clogged. Instead, it is the fuel pump losing suction when the fuel is low. Which means the fuel pump diaphragm could have been weakened or has a small hole in it or an air leak somewhere in the fuel system.
When tank is full or high, there is positive pressure at the bottom of the pick up tube. And the weakened fuel pump is able to deliver. However, when the fuel gets low there is no more positive pressure and the weakened fuel pump in unable to deliver anymore or because a small air leak is preventing it from doing so.
If you had the clear fuel filter you should see bubbles when the fuel pump struggles to deliver if the cause of the problem is an air leak. If there are no bubbles, then it could just be a weakened diaphragm.