Just to keep stuff up to date here....
I have been trying a number of things suggested to me on the ZoneLabs forum, including giving trusted server rights to the avast program, and to all browsers, but it doesn't seem to change the behavior much.
I must say, as much as I like avast, I suspect that the problem is on the avast side. My reason for this is that I notice the following behavior:
1. With a clean boot, running ONLY avast and Zonealarm, and no other non-microsoft services, after a period of moderate web surfing, the browser will hang.
2. If I terminate the avast web shield, I don't even have to restart the browser. I can just press the reload button, and everything works fine.
3. If I try to re-start the web shield, it won't fully restart. It will go into a state where it says "The Provider is waiting for a subsystem to start".
4. If, when the browser hangs, instead of terminating Avast, I terminate ZoneAlarm, the problem does not go away until I reboot.