I heard back from Network Solutions about this issue. Their response was basically:
Our SSL proxy doesn’t allow server-side variables to detect HTTPS (secure). All server-side coding will always detect HTTP (non-secure), and for programs that attempt to redirect non-secure connections (http://) to a secure connection (https://) will result in an infinite loop and server error after 30 seconds (newer technology browsers such as Firefox will detect this loop almost immediately and give up before 30 seconds). We cannot change this setting on our servers.
There is a 2nd paragraph with their recommended workaround, which is similar to my approach above of looking for ‘https:’ in the scheme of the URL.
I’m going to see if the bbPress developers would include the above code in their core. Seems like a worthwhile addition, or maybe they are aware of this and intentionally do not include it for various reasons.