Is it possible to tweak AES-GCM so that it is satisfactory for whole-disk encryption (like XTS mode)? Is it possible to leverage a preexisting implementation of AES-GCM to provide the key security benefits essential for full-disk encryption (similar to AES-XTS)?

GCM is a popular encryption mode supported by several libraries and with fast implementations in hardware, and on its own GCM has nice properties including parallelism. Because of GCM's built-in authentication functionality and due to its performance, it is beneficial to consider that as a starting point; a hardware implementation may implement AES-GCM as a self-contained performance routine.

But on the other hand, a critical requirement of GCM (essential to its security) is that it must have unique random IVs, just like CCM. So if the IV that is chosen is derived from the sector or block offset (even if there's an intermediate hash), the very fact that on a disk it's common to write and overwrite data in place (coupled with GCM and CCM behaving nearly like stream ciphers) makes it potentially dangerous to derive the IV in that deterministic way. But just like many encryption modes are based upon compositions of cryptographic primitives, I'm wondering if it's possible to start with GCM (and its AEAD property) and build upon that to also attain the secure capability of writing to disk at sector offsets.
The ZFS file system uses AES in CCM or GCM modes.  This works because in ZFS the data and file system metadata is encrypted but the block pointers are in the clear, the AuthTag (MAC) is stored in the block pointer.  ZFS also has a SHA256 based merkle tree based on the block pointers that is used for data integrity for resilvering and navigation purposes.

Note that ZFS is file system (actually object based really) encryption it does not claim to be "full disk encryption".

For more details see here: https://blogs.oracle.com/darren/entry/zfs_encryption_what_is_on

Darren J Moffat (Architect and lead developer for ZFS encryption).