How can I isolate grounded (neutral) conductors in a panel?
Yes, the neutral bar should be isolated from the case and all neutrals should be connected to an isolated bar. 

You can purchase another bar with isolation mounts and connect it (with a heavy-gauge [4Ga is  typical] white wire) to the first neutral bar if needed to provide adequate neutral bar space. Likewise for a non-isolated ground bar, if needed. NOT having to do this sort of foolishness is one reason for leaving adequate wire in the first place, but presumably whoever wired this wrong was also of the "I want it neat and tidy and no excess wire" mindset.

This question and answer might provide some insight and pictures to look at:
Can I extend the ground/bus bar in a main service to accomodate subpanel equipment ground?