I don't believe your argument is correct. What determines the lift and
drag coefficients is angle of attact, NOT airspeed. The inner wing is
flying at the same angle of attack as the outer wing, think about it.
Speeding up won't make you climb better.

In fact, the inner wing is not flying at the same airspeed. It has the
same angular speed, but it is transribing a smaller circle than the
outer wing and thus going a shorter distance in the same amount of
time. Both wings are sinking at the same rate, therefore, since the
tangential (straight line) speed of the inner wing is lower, its angle
of attack is higher. Same thing happens at the wheels of your car,
which is why you need a differential gear, to accomodate the
difference in speed between the inside and outside wheels during a
turn. The outside wheel travels a greater distance, though both have
the same angular speed.