Just had a look at the settings I used the last time I wanted smooth white noise.. turns out I actually used brown noise, then high-passed it around 1.3k with strong-ish resonance. I didn't actually take any of the high frequencies out - it was the high-passing that seemed to do the most to make it sound smooth.

I made the patch in Alchemy and just used 1 instance of brown noise as the signal source.

I take it the problem is nothing to do with clipping or with resonance being cranked all the way up or something like that?

Just check the channel meter on whatever your DAW is. Sylenth has its own internal meters too, but I don't know if there's any clipping risk from hitting the red on those. The answer seems to be no from my experience, but probably best to get someone more knowledgeable to verify that.

Did you even eq and use a filter?