It does not work like that. The wave function of 6 electrons is the product, not the sum, of orbitals (wave functions of a single electrons). However, since electrons are fermions the overall wave function must be antisymmetric. Thus, the simplest wave functions that you can write (in the spirit of the H"uckel method) is the Slater determinant: $$\psi({\bf{r}_1,\ldots,\bf{r}_6}) = \left| \begin{array}{cccccc} \phi_1(r_1) \alpha(1) & \phi_1(r_1)\beta(1) & \phi_2(r_1)\alpha(1) & \phi_2(r_1) \beta(1) & \phi_3(r_1)\alpha(1) & \phi_3(r_1)\beta(1) \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \phi_1(r_6)\alpha(6) & \phi_1(r_6)\beta(6) & \phi_2(r_6)\alpha(6) & \phi_2(r_6)\beta(6) & \phi_3(r_6)\alpha(6) & \phi_3(r_6)\beta(6) \end{array} \right|$$ where $\phi_k$ are the H"uckel single electron wavefunctions (the orbitals), $\bf{r}_i$ is the position and spin variable of electron $i$, and $\alpha(i)$ and $\beta(i)$ refer to the spin function (up and down, respectively). The Slater determinant has 6 rows: you change the electron index in each row.

Following the simple H"uckel theory the energy of the system is $E = 2(E_1 + E_2 + E_3)$ where $E_k$ is the energy of the orbital. (Of course this is a rough approximation that doesn't take into account interelectron repulsion or double counting these repulsions if they are included in some averaged way in $E_k$.)

Therefore the time-dependent wave function is $\Psi({\bf{r}_1,\ldots,\bf{r}_6},t) = \psi({\bf{r}_1,\ldots,\bf{r}_6}) e^{-iEt/\hbar}$

It does not work like that. The wave function of 6 electrons is the product, not the sum, of orbitals (wave functions of single electrons). However, since electrons are fermions the overall wave function must be antisymmetric. Thus, the simplest wave function that you can write for the 6 electron-benzene approximation (in the spirit of the H"uckel method) is the Slater determinant: $$\psi({\bf{r}_1,\ldots,\bf{r}_6}) = \left| \begin{array}{cccccc} \phi_1(r_1) \alpha(1) & \phi_1(r_1)\beta(1) & \phi_2(r_1)\alpha(1) & \phi_2(r_1) \beta(1) & \phi_3(r_1)\alpha(1) & \phi_3(r_1)\beta(1) \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \phi_1(r_6)\alpha(6) & \phi_1(r_6)\beta(6) & \phi_2(r_6)\alpha(6) & \phi_2(r_6)\beta(6) & \phi_3(r_6)\alpha(6) & \phi_3(r_6)\beta(6) \end{array} \right|$$ where $\phi_k$ are the H"uckel single electron wavefunctions (the MO-LCAO in H"uckel's approach), $\bf{r}_i$ is the position and spin variable of electron $i$, and $\alpha(i)$ and $\beta(i)$ refer to the spin function (up and down, respectively). The Slater determinant has 6 rows: you change the electron index in each row.

Following the simple H"uckel theory the energy of the system is $E = 2(E_1 + E_2 + E_3)$ where $E_k$ is the energy of the orbital. (Of course this is a rough approximation that doesn't take into account interelectron repulsion or the double counting of these repulsions if they are included in a self-consistent way in $E_k$.)

Therefore the time-dependent wave function is $\Psi({\bf{r}_1,\ldots,\bf{r}_6},t) = \psi({\bf{r}_1,\ldots,\bf{r}_6}) e^{-iEt/\hbar}$