Inf means "infinite". I wouldn't call that a "best case scenario".
I think maybe some/most/all miners aren't bothering to include any no-fee transactions in the reserved section of blocks anymore.
You are almost certainly correct.
I asked the 21.co guys and they said they might try to improve that portion of their fee reporting page.
You're looking for them to report a time that is longer than infinity?
I don't think so but will my Armory wallet eventually timeout or something automatically
No, it will not.
or will I have to take deliberate steps to rectify the situation?
Yes, you will.