I do not know at all how do you model electric propulsion, but I wonder that you assume some sort of continous thrust as:
$\ddot{x}=3n^2x+2n\dot{y}+u_x,$
$\ddot{y}=-2n\dot{x}+u_y,$
$\ddot{z}=-n^2z+u_z,$
where $u_x$, $u_y$ and $u_z$ is the continous action. In a matrix form it can be written as
$\dot{\mathbf{x}}=\mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u},$
where I assumed that $\mathbf{u}$ is the thrust and can have any time-dependency. This is a linear-time varying system which has the following analytical solution
$\mathbf{x}(t)=e^{\mathbf{A}t}\mathbf{x}_0+\int^{t}_{t_0}e^{\mathbf{A}(\Delta T - \tau)}\mathbf{B}\mathbf{u}(\tau)d\tau$,
where $\Delta T=t-t_0$ and the term $e^{\mathbf{A}t}$ is the state transition matrix (which for the HCW equations it has a closed form).
Now, the issue is to solve the integral of the control term, which depending of the assumed time evolution of $\mathbf{u}$ will have an analytical solution (e.g. if the thrust is assumed to be constant) or not. However, if an analytical solution is not possible, it can be integrated numerically.
What I wanted to remark is that HCW equations can be extended to continuous thrust models.
For your second question, you must consider that there are different types of AOCS thrusters depending on the type of operation, so the nominal situation is that you will be carrying on-board thrusters capable of providing the $\Delta V$ with the required accuracy.
