I just thought I'd post a followup on what I found.
It appears that if you put in a couple more ACL lines, you can achieve what I was looking for:
acl HTTP proto HTTP
always_direct allow HTTP
This will cause all queries to go directly "through" the proxy, without checking the cache. That way, if the drive fails or something goes drastically wrong, you can have a fresh install of Squid, configured with this, to take over until you can get things figured out, and no reconfiguration of the client browser is necessary.