First off, it is not possible to convert from a PSD to the time domain directly (and retrieve the original random input signal used to create the PSD) as the time information has been lost when it was originally converted to the frequency domain. What you are most likely doing to get this random time signal is taking a sampling of sort from the PSD curve and creating a random signal that way. This is fine so long as you do this for a long time, such that the signal is accurately represented statistically. For example, imagine if you only converted .1 second worth of random signal from the PSD to the time domain. Would this be long enough to accurately represent the full random input? Probably not, you would likely need hours of data.
I am highly doubtful that the second of time you show above is anywhere near long enough to fully represent the signal. This is why the PSD method was introduced to begin with as it was impractical to analyze in the time domain; the duration required to capture the full response is far too long! You will likely want to rethink your approach to this problem. Is there some way to add in your sine tones and then convert back to PSD (while still retaining the intended sine tones)? My initial thought is that this is not possible, but I'm not fully certain. Why not try and contact Tom and get his thoughts? You might need to pay for some consulting service for an hour or two, but I'm sure that will be worth it considering the time you would save.
As for the non-linear analysis, you can expect a very long solution time, depending on the complexity of your model. You are essentially multiplying the linear solution time by the solution time of one frequency of non-linear analysis, i.e. X minutes for the linear solution * Y minutes for one iteration of the non-linear solution at one frequency * Z iterations to convergence). You can see this will likely be quite a long process. If your model is simple enough it may not be a big deal, but my experience is you generally need a descent size model to get good results regardless of the problem being analyzed. Good luck! Let us know what you come up with.
Did yu finally find out how to do it?
I am having the same troubles...