I'm running 8 x64 Release Preview. I just reinstalled 8RP about 2 hours ago and downloaded Avast fresh this evening. It is 7.0.1474. My system crashed with the same BSOD relating to aswnet.sys three times in about 30 minutes. I disabled all shields about 45 minutes ago and experienced no more crashes. About 15 minutes ago I enabled all shields except for the web and network shields, since I've read it could be either, and so far it hasn't crashed again. I'll look for the dump file to upload. The only apps I have installed are Keepass and Firefox. I crashed twice before installing Firefox. One crash just moving around in Windows, one crash was when I tried to start the installer for Fx, and once after installing it when I tried to start it. Keepass was installed after the crashes.
EDIT: I uploaded "Ignotus mem dmp.zip". This is a dump before I changed Windows to do a complete dump. I had a crash after changing to complete, but there wasn't a dmp file to upload.