The number of iteration in the default setting is enough for most of our test case. If you want to increase the iteration, you should mimic the code block from pm.sampling - currently there is no easy way to change it.
In general, ADVI initialization is good to some extent: the problem is that it underestimates the variance which just results in the subsequent NUTS with small step size. So it is hard to say for sure if running ADVI longer would improve NUTS.
If you have correlated latent variables, you should try to reparameterized the model. Maybe you can try modelling the additive outlier cases as a state as well?