What is the networking layout for the IPSpace they want you to use? Is it just another subnet, or a actually separated network? Either way, I wouldn't rebuild volumes. I'd create the IPSpace, set up the vFiler that you'll be moving to, and then move the volume from the old vfiler to the new one. You should pre-sync the /etc system files you use (like exports, or maybe passwd and group). Here's how I'd do it:

-Create the new IPSpace. If it's physically separate networks, you'll need to free up an interface to connect to the new network and allocate that to the IPSpace. If it's not a separated network but just another subnet, you can assign vlans from an interface to separate IPSpaces.
-Create a new root volume for the new vFiler and leave it in the default vFiler (on the default IPSpace) for now, and import everything you need from the running production vFiler with ndmpcopy or something.
-Create a new vFiler inside the new IPSpace on the new root volume you created. You'll need to make sure that /etc/rc has a line in it to define a default gateway on that IPSpace, which means adding a vfiler run route add default line. You only need one of these per IPSpace in the /etc/rc file. Make sure this vFiler is capable of doing everything your production vFiler does. Install a new ESX server if you have to to test that everything it will need is there before you pull the trigger.
-During the migration, halt any IO to the old vFiler, disable it, and then move the volume to the new vFiler. Once it's there, you might need to do some setup on the new vFiler and possibly ESX servers to make sure that they can use the datastores properly.

When I did this, I wasn't moving VMWare- we have that going over FC to vFiler0. I did have to do this for a bunch of CIFS and NFS vFilers, though. Let me know if there's any further clarification I could provide!