Taking the disk out of its case is a bit of a faff and may invalidate the warranty of the drive. Connecting it to the HDR-FOX main board and using the 'gpft' option from maintenance mode will work, giving you a large partition in EXT3 format, but this will also give you two extra unwanted partitions (1 and 10 GB, respectively).
If you want your external drive in NTFS format with GPT, you should be able to do this on a Windows PC using the Disk Management console. The option to convert to GPT is only available when the disk is unallocated. I have found the easiest way to create a GPT drive is to use Diskpart (command line tool) to assign the disk as GPT and then format with Disk Management. I did this on a PC running Windows 10, the method is as follows:
Connect the drive to the PC by USB, then open a command prompt (admin). Type the following commands:
Diskpart (opens the Diskpart program)
List disk (lists all connected drives with their allocated numbers: the disk for conversion was disk 1)
Select disk 1 (changes the selected disk to disk 1: substitute whichever number corresponds to your drive), you will get a confirmation
List disk (to check that the correct disk is selected)
Clean (wipe disk configuration and convert the drive to unallocated: THE DISK WILL BE WIPED WITHOUT ASKING FOR CONFIRMATION - ensure that you have selected the correct disk first!)
Convert gpt (will mark the disk as GPT)
List disk (to check that gpt is selected)
Open Disk Management:
Right click on the 'unallocated' partition of your drive then select 'New Simple Volume' (if nothing happens, eject the USB drive, then reconnect and try again.
Click 'Next' x3
Give the volume a label, if you like. Make sure 'Perform a quick format' is selected (otherwise formatting will take ages), then 'Next' and 'Finish' (the default format for a large drive is NTFS).
If you wish, return to Diskpart and type 'List disk' (this will confirm that the volume is still GPT)
Exit Diskpart, close command prompt and exit Disk Management.
I don't have a large (>2TB) to test this on but it worked with 1TB USB drive and a 16GB USB flash drive. If you try it on a large drive, please post to let us know how you got on.