I wanted to create a new topic about "The vocal thickening trick (VTT)" before I noticed your topic. Therefore, if you do not mind I will add my improvements right here.
First, I want to say that I had never faced any issues like you mentioned, but that probably is because I only use the default settings. Except for the tuning variable, I do not change the anything. Probably that is the reason why I do not fall into the resonance artifacts.
However, your explanation makes perfect sense. It is a fact that prime numbers are only divisible by one and the prime itself, so indeed, like you wrote, you do not get them synchronized. Never thought about it actually. Thanks for sharing!
About the improvement that I use:
Warren illustrates the VTT by literally copying the track several times, but what if you edit a word or sentence of the source, later on in the session? It means that you have to copy the edited version again to the other tracks.
What I like to do instead is to create four stereo FX channels with the Waves - Doubler inserted. Then I use four channel sends on the source track and route them to the input of the four FX channels. If you make changes to the source now (Edits, EQ, whatever), it instantly also affects the VTT. It works a lot more convenient for me.