Perhaps sharing my experience can provide you with that direction. I contacted Avast about a refund for Grimefighter on 12/22/14. I received no response after two weeks and submitted two more tickets (1/6/15 & 1/13/15) - still no response. I followed up with a complaint on 1/21/15 and navigated my way through their phone system in an attempt to speak with anyone who could provide any information. An Avast associate named Andrew advised me to continue waiting. He explained that refunds were handled by Avast headquarters in Prague and that nothing could be done about it. When I asked for contact information for the Prague offices, he tried to dissuade me from pursuing the matter any further, on account of the language barrier and the cost of phone calls to Europe.
It was at that point that I contacted the Better Business Bureau - specifically the San Mateo office (where Avast is located in the US.) I filed a detailed complaint with them on 1/23/15. By the following week, I finally received a response from Avast and the refund was processed.
How much of a hand the BBB had in this matter, I don't know; it certainly can't hurt to involve them. I'm sure you've looked through these forums and seen how many customers have encountered the same problem that we have. Perhaps enough complaints to the BBB will encourage them to take this matter up with Avast and force some positive changes, like more responsive customer service.
On a side note to any moderators that would like to weigh in: I am aware that you provide valuable advice on how to better navigate the refund process in these forums, but they are not always the first place dissatisfied customers look. If that information was available on the Avast website when I was filing my support ticket, I could've avoided having my ticket bumped to the back of the line every time I submitted a new one. I feel that clearer communication at the support-ticket-submitting step of the process could potentially reduce the amount of times that you have to re-explain the refund procedure here on these web boards.
Hope that helps.