sorry chums I'll sit this one out
Without knowing the technical side of it I'd say, that's would be a pretty brilliant solutionPerhaps beg @SheepCow to make a mod where we can post-process a thread, i.e. So if a player posted on a game thread it would take his post, delete it and repost it as Guest: Character for specified threads.
Personally (i.e. Not as a mod) while I get the idea I'd have to say I use FH on mobile these days and logging in out would be a pain in the arse. You'd miss notifications for example.
As a mod security issues of shared accounts are bad in general and there's nothing to stop people doing daft things like linking their Facebook account to the shared FH one, etc.
Perhaps beg @SheepCow to make a mod where we can post-process a thread, i.e. So if a player posted on a game thread it would take his post, delete it and repost it as Guest: Character for specified threads.