Fast transient simulation of steady state

Hi,

I would like to see the actual (i.e., not small signal) steady state response to an integrator (e.g., to get HD3). By construction, it has a huge time constant:

I would need to simulate quite long until this reaches steady state and even what's shown above is already many minutes. Very long just to get HD3.

I am aware that I can set an initial voltage to some node. But this only works if my signals are the same all the time. But I want to sweep over frequency, which makes the steady state voltage over the cap different all the time as well as different input voltages.

Is there any meaningful way to circumvent that?

I would also use PSS ... but my experience shows I cannot really trust PSS ... tran with tight tolerances is just the "golden reference".

And even then, it only shows me one period, not enough for plotting the DFT and evaluating linearity + HD3.

Well, I could obtain IIP3 and obtain HD3 from there but again: My experience shows me that I cannot trust this unconditionally and while they are similar, the HD3 obtained through IIP3 measurements are always off by  a couple of dB from a tran HD3 value.

Is there maybe an automated to let PSS calculate the steady state point and use this result as initial conditions for tran?

Or anything else that could help speed this up?