$\tilde b^{el}_R$ mix with just one composite multiplet each, $\tilde u^{cp}$ and $\tilde b^{cp}$ respectively. In this case the Yukawa couplings of the top and bottom sectors are generated by terms involving different fields $$\label{yukawa2}
{\cal L}_{cp}\supset-y_{cp}^t\bar q^{1cp}\Sigma \tilde t^{cp}-y_{cp}^b\bar q^{2cp}\Sigma \tilde b^{cp}+{\rm h.c.} \ .$$ The top and bottom Yukawa couplings are disentangled and, after diagonalization of the elementary/composite mixings, we get $$\label{yukawa3}
y_t=y_{cp}^t\sin\theta_{q1}\sin\theta_{t} \ , \qquad y_b=y_{cp}^b\sin\theta_{q2}\sin\theta_{b}\ ,$$ with each Yukawa controlled by a different Left-handed mixing angle. The small bottom mass arises as a consequence of a small $\sin\theta_{q2}$.

To implement the previous idea we modify ${\cal L}_{mix}$ and consider two mixing terms for $q_L^{el}$: $$\label{lmixq12}
{\cal L}_{mix}\supset \bar q_L^{el}(\Delta_1 {\cal P}_{q_L}q^{1cp}+\Delta_2 {\cal P}_{q_L}q^{2cp})+\rm{h.c.} \ .$$ Another possibility is to introduce two elementary fields $q_L^{1el}$ and $q_L^{2el}$, both transforming as ${\bf 2}_{1/6}$ under \[SU(2)$_L\times$U(1)$_Y$\]$^{el}$, and each mixing with the corresponding composite field $q^{1cp}$ and $q^{2cp}$. To get read of one elementary doublet we introduce a Right-handed doublet $q_R^{el}$ with the same quantum numbers as $q_L^{1el}$ and $q_L^{2el}$, together with a mass term marrying $q_R^{el}$ with a linear combination of the Left-handed elementary doublets $$\label{lmassq12}
{\cal L}_{el}\supset m_{el} \ \bar q_R^{el}\ (q_L^{1el} \ \cos\gamma-q_L^{2el} \ \sin\gamma)+\rm{h.c.} \ .$$ 