Generalized KPR: Frisch Elasticity
Regarding the presence of $l$ in the Frisch elasticity, your result is correct. It is my impression that a Frisch elasticity free of $l$ requires very specific functional forms.

For example we know that the following utility function 

$$U(c,l) = ln(c) +\alpha \frac {(1-l)^{1+1/v}}{1+1/v} \tag{1}$$
gives a Frisch elasticity independent of $l$ (and then $\eta=v$).

We could compare this with your utility specification and say "ah, so we must have additive separability to obtain a Frisch elasticity independent of $l$"...
No, this is not enough. Note that essentially $(1)$ does not express utility as a positive non-linear function of leisure but as a negative non-linear function of labor, and so the term $1-l$ appears. This is critical to eliminate $l$ from the final expression.  

Because, if  we assume additive separability in general, then the cross-partial derivative is zero and we would be left with

$$\eta = \frac{u_l}{- u_{ll}}\frac{1}{1-l} \tag{2}$$

If the additively separable utility function is expressed as a non-linear positive function of $l$, and not as a negative non-linear function of $1-l$, $(2)$ would also be dependent on $l$.

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Also, with your utility function specification, I do not find that $\sigma$ is out of the final picture. Instead I find

$$ \eta = \frac{\gamma(1-\sigma)-1}{(\omega+\gamma)(1-\sigma)-1}\frac{l}{1-l}$$

If $\omega = 1-\gamma$ this simplifies to

$$ \eta = \frac{1-\gamma(1-\sigma)}{\sigma}\frac{l}{1-l}$$

But these are treacherous algebraic calculations - you should recheck.