Hightower have you got to the bottom of this!
Long story on my fuel problem was solved by changing primer bulb.
I then dissected the bulb and found one of the non return ball (inlet side) was sticking shut preventing the flow from tank to engine, causing the bulb to collapse and stay collapsed. Eventually the engine suction dissipated and the bulb would return to shape and would work again for a few days. Caused, I think by over tightening of jubilee clip, distorting plastic tube, hence ball getting stuck.
In your case the bulb goes soft with the engine running, perhaps the ball (inlet side) will not close when bulb squeezed, thereby you are pushing fuel back down to your tank. (Five quick squeezes of the bulb would beat the engine draw and the bulb should be firm!)
What causes your engine to stall at low revs!!!!!!!!!! Could it be the non return ball (outlet side) is sticking shut when engine is not pulling for fuel at its strongest point ie low revs. This may have been caused by over tightening of jubilee clip outlet side.
Starting to confuse myself now, but having dissected a bulb, it gives you a clearer understanding of how they work and what gives the most grief. I'm sure sticky residue in fuel and distorted orientation of bulbs cause many combinations of 'sticking balls'