GARCH simulation - user-supplied disturbances

I would like to simulate a GARCH time series, and have some questions about the GARCH functions in the Econometrics toolbox.

The only options for the conditional distribution within the GARCH specifications are a normal distribution or a t distribution. I would like to supply a matrix of user-generated conditional disturbances (following a generalised lambda distribution). Am I right in thinking that this may be done via the 'State' input?

I would like to be able to specify a starting value for the time series' conditional variance. Am I right in thinking that this is done through the 'PreSigmas' input? Will I then need to specify 'PreInnovations' and 'PreSeries' as well?

One important issue within the model is random number control - I want to ensure that I can trace any differences in outputs back to differences in inputs, not the random number stream. With this in mind, I'm wondering if there is a risk of having my user-specified disturbances (via the 'State' input) altered. I'm not clear how the 'Tolerance' input works, especially where starting 'PreSigmas' values are prespecified. Does 'Tolerance' still have any impact under this framework? Is there a risk of the model pregenerating random values in order to force a steady state time series?

I note that the 'State' input specifies that the contents are standardised, with zero mean, unit variance and iid. Are there any practical consequences within the code if this is violated?

Many thanks.