I'm still thinking about this, but I am not sure I agree/understand...
I need to increase lift to stay in a level turn so instead of increasing speed, I increase angle of attack and that in turn will increase my stall speed.
Yes, for a given angle of bank, which corresponds to a given G load, there will be a stall speed increase. Ignoring changes in configuration (flaps, slats, ice) the angle of attack at which that airfoil stalls is proportional to the lift it must create (weight X G), but nothing else. If for a given condition of flight, the pilot increases the angle of attack, the pilot takes that wing closer to stalling, but the speed at which the stall occurs is not changing
because the angle of attack is changing. If the change of angle of attack (with no other configuration changes) resulted in a change of the stall speed, the angle of attack indicator would not really be a useful indicator of the approach to the stall.
If stall speed changed relative to angle of attack, it would be necessary for flight manuals to contain stall speed charts for angle of attack in addition to stall speeds for angle of bank. Then every aircraft would have to be equipped with an angle of attack indicator so the pilot could apply that chart.
The section of airfoil at any spanwise point along the wing (and in co-ordinated flight) does not know if it is in level or banked flight. It just knows it is reacting a given load (weight X G). It knows its angle of attack, and how close it is getting to its Cl max, but it will wait to get to that Cl max before it stalls. Increasing angle of attack takes it closer to that Cl max and the stall. but does not change Cl max, so the stall speed is not being changed.
When you "go ballistic" over the top of a push over, it is possible that you are not reducing the angle of attack as the pitch attitude of the aircraft (relative to earth) reduces. You have, however dramatically reduced the stall speed, as you have reduced G, and the demand for lift.
I'm not asserting my expertise on the foregoing, but it is what I have understood from training from several sources...