OK, first of all, the AOA on the root of the prop is higher than the tip, not lower. This is, as I said before, to compensate for the reduced airspeed at the root, to maintain a constant amount of lift throughout the entire prop blade. Second of all, a stall is not dependant on airspeed at all. It is important to remember that the word "stall" is completely independant on how much lift is being created. A stall will always occur at the same AOA for a given airfoil. This is called the "critical angle of attack", or CAOA. At the CAOA, the coeffecient of lift (CL) is at its max. Anything beyond the CAOA, the the CL decreases. At this point, an airfoil is stalled. You are correct, however, to say that the CL generated by an airfoil is reduced as airspeed is decreased, unless the AOA is increased to maintain the same CL. If you were to look at a CL vs. AOA graph, you will see that an airfoil is stalled only at the AOA's higher than the CAOA. If the graph you are looking at is of a symmetrical airfoil, you will see that CL is zero when AOA is zero, no matter what the airspeed is, but this is not a stall. This is merely insufficient lift. CL is less than the weight of the aircraft, and the aircraft will not fly, but is not stalled.
By the way, I am a flight instructor by profession. If you have any other questions, or I have confused you an any way, feel free to ask, and I'll see if I can clear up anything. Also, you can consult "Flight Theory For Pilots" by Jeppesen, and you can see all of the math to goes into this if you are interested.