I have the same Conti's DWS-06s (size 265/35ZR20) on my wife's '15 Audi Allroad (AWD), and recently, about two weeks ago, had one tire replaced due to non-repairable puncture in the tread. I have noticed a similar behavior with the new tire, so it's likely the tire itself, and not a balance issue.
When on the highway, the vibration is not noticeable (in the PNW, the roads get physically worn-out and grooved. so you worry more about tramming issues.) However, I noticed a harshness (it's on the right front) when I'm in sweeping turn on a road leading to the highway, which is older aggregate pavement, with a road speed of 35-45 mph.
Hope this helps.
2017 Q60 Red Sport AWD Iridium Blue / Monaco Red / Premium Plus Package 3.0t Sport / Infiniti Sport Mats / FI Full Catted DPs & CBE / Stoptech Trophy BBK FR & RR w/SS-Braided Brake Lines / Infiniti HE / Infiniti Intakes / AMS HPFP / Ecutek Tune / BMS Pedal Tuner / Infiniti Radiant Sport Grille / EMM Tuning CF Foglight Finishers / CF Duckbill RR Spoiler / Mishimoto OCC / Stillen Rear Stab Future: AMS LPFP / AMS CF DS / Z1 LSD / Vorsteiner 20" VFF 112s (Staggered) / Michelin Pilot 4Ss