The resonant frequency is the geometric mean of the upper and lower half power frequencies, not the arithmetic mean you seem to be using here.
\$\omega_0 = \sqrt{\omega_l \omega_h} \ne \dfrac{\omega_l + \omega_h}{2}\$
That's probably all you need but here's some additional information just in case.
[UPDATE: upon further reflection, there's something else you need. The relationship between Q and BW you are using is a high-Q approximation. Deriving the genuine Q from this approximation requires a bit more than I've given below.]
For a series RLC, we have:
\$ Z = \dfrac{1 + j \omega RC - \omega^2LC}{j \omega C}\$
The numerator is of the form:
\$ 1 + j\frac{1}{Q} \frac{\omega}{\omega_0} - (\frac{\omega}{\omega_0})^2\$
Comparing these two forms, see that:
\$ \omega_0 = \frac{1}{\sqrt{LC}}\$
\$ Q = \dfrac{\sqrt{\frac{L}{C}}}{R}\$
How to see that the resonant frequency is the geometric mean?
Consider the product of two first order functions:
\$ (1 + j\dfrac{\omega}{\omega_l})(1 + j\dfrac{\omega}{\omega_h}) = 1 + j \omega (\dfrac{1}{\omega_l} + \dfrac{1}{\omega_h}) - \dfrac{\omega^2}{\omega_l \omega_h}\$
From this, we deduce:
\$\omega_0 = \sqrt{\omega_l \omega_h}\$
\$ Q \omega_0 = \omega_l || \omega_h =\dfrac{1}{\dfrac{1}{\omega_l} + \dfrac{1}{\omega_h}} \rightarrow Q = \dfrac{\omega_0}{\omega_l + \omega_h}\$
