Generally speaking when analysing the noise of a clocked system, you would do the PSS analysis with just the clock present, and not a large-signal input present too. This means it will then do a small-signal analysis of the noise with the aliasing and noise folding caused by the sampled data system itself - and will also be a lot faster as you then don't need to include the 1kHz signal in the PSS solution.
If you do include the 1kHz signal as a large signal input, you'll be able to see the intermodulation of the noise with this large 1kHz signal too - normally that's only important if the large signal input is large enough to create distortion - because then you might get intermodulation with these distortion harmonics which could impact the noise performance - but for most normal situations there's no need to have the large signal input. Think about how you'd analyse the noise for an opamp; you wouldn't normally have a large-signal input present at the same time.
If you do have 1kHz signal input, this will cause flicker noise to mix with the 1kHz signal and its harmonics. Given that flicker noise is infinite at 0Hz (as it is 1/f), you'll end up with an "infinite" (or very large) noise at multiples of 1kHz. Since your frequency sweep may not exactly hit the multiples of 1kHz, you'll probably just see peaks.
So I'd try again without the 1kHz large signal being present.