I just tried deleting the support.avast cookie. No difference.
WRT OpenDNS, I would not bother since support.avast.com is the only site that the anomaly occurs. Some days I can get to the site and other days, I cannot.
I just did two traceroutes. For
www.avast.com (67.228.112.194), I am taken to the US west coast.
For support.avast.com (195.47.75.66), I am taken to the Czech Republic.
Since I use Visualroute, I can supply screenprints if required.