What could be the cause of this/ just replaced, coils, what now? Thanks for any info!

what do you mean by shimmy?, you mean you feel slight shaking?

no, like "shimmy shimmy coco wha?! light it up and smoke it,pass it to me now"
... I mean like ye, slight shaking

I am not sure if shimmy means vibrations,

but on my VQ35DE since new, at about 3800-4000rpmswith no throttle in gear, i get weird vibrations....

I use amsoil 0w30 series 2000 oil, and my car has seen synthetics since 5K now i have 70K