Hi.
If you user the caret ^ in a rule it means "start with" and the rule won't work if the site is under a folder (like in your first example). But if you plan to move the site on root once ready, and you don't want to change all the rules, there is a better way. In the plugin settings (advanced) you can put a path (e.g. /hhhblogs) that is excluded from the process of checking rules. Once you are ready to move the site, you just blank this field and the rules continue to work.

I can't see any other problem in your rules, but let me know if I'm missing something.

Best
Luigi