mode_compute=5 with optim={'Hessian',2} relies on the outer product of gradients and requires the use of a univariate Kalman filter. Therefore, something similar is not available for other optimizers. As Stéphane indicated, mode_compute=6 also differs.
The reason for using the inverse Hessian at the mode is that this is the most efficient choice if the posterior would be normal. But any positive definite matrix for the proposal density will do. You could provide any arbitrary matrix via the
command.