Sinking concrete pier: Better to not attach new post to pier?
To meet modern best practice you'd want both ends of any post anchored. Obviously your particular home isn't going to collapse if a post was to fall out (and it's unlikely it could anyway with that small of a gap). 

To slightly derail the conversation, I'd seriously consider permanent adjustable floor jacks for your purposes. Why not build some future-proofing into your solution (assuming you aren't opting to dig proper footings)? They aren't terribly expensive (for the few you want to fix), and they'll allow you to add height down the road as needed.