I haven't migrated using the VM Data screen but it should be possible because I have changed the Data Storage and High Performance on my ESM as well. Basically it stops dbservice, cpservice, creates the new filesystem and starts a copy of the files to the new partition.
Another way can be a more hardcore version :-)
I assume you new SAN is mapped a new data store in vmware, right ?
Why not change the data store of the ESM VM to the new SAN, enlarge the disks from VMware and then grow the partition + file system :-)
So... I see two ways of doing this :-)
In any case it's easy because you have snapshots...
I have done this before, and other than a problem in 9.5 with the script that does the actual copy, it worked fine. We moved originally from the VM to an additional disk, and then like you, needed more space and migrated to a larger disk.