WUP installer is NOT working with FAT32 USB at all (like I said on the second post of that thread in answer to "the similar issue than the OP" like you said)
if you install a game to the "fake SD redirected to USB using Mocha beta" bug, then your installed game will have only 0byte files size.
you posted in that thread, and you specifically said you have the same problem (meaning, problem using a FAT32 USB ! not a WiiU formatted HDD), so I assume you are using Mocha to get a FAT32 USB on your WiiU.
if your problem is about wiiu HDD (not FAT32 HDD), then I'm not sure it was a good idea to post in someone else's thread about a different problem.
Personally, I never understood why users post on someone else thread, saying "I have the EXACT same problem" and knowing the solution for that EXACT same problem has already be given, but in fact it's completely ANOTHER problem.
If it's the SAME problem, then the solution has been given, and you fixed your problem by reading the answer provided to the user who created that thread and already fixed it.
if the provided solution doesn't work for you, then it's obviously NOT the same problem, then why use a someone else thread with a different problem to get a completely different help?
About your actual problem, based on what you said:
The Wii U USB External HDD is fully formatted by the Wii U (using the message that pops up when a USB device is connected first time)
So, it's not FAT32. ok.
It's a Toshiba 3TB Powered USB HDD, there is no multiple partitions. However before the Wii U formatted this HDD, I did a format prior on my PC using a non-Windows formatting software tool to make the HDD 2TB leaving the remaining 1TB unallocated. I was under the impression that HDD have to be 2TB and under for the Wii U to recognize it.
Partition size is different than drive size. if the WiiU has a drive size limit, formatting a smaller partition will have no effect on the compatibility restriction.
All the thing you did on PC to format or partition the drive has been lost and has no effect, because the wiiU completely deletes the partition table (sector 0 of the drive) and there's no more partition when formatted in WiiU format. all the drive is "raw encrypted".
I just upgraded to this HDD this weekend from a 500GB drive. I transferred all the data over using the copy and move feature in the Wii U settings.
Ok, so it means it worked fine.
After that I used the Mocha CFW after every reboot
Why Mocha?
even if you don't have Haxchi, or CBHC installed, there are better alternatives than Mocha as CFW.
If you have Haxchi or CBHC, you don't even need Mocha because you ALREADY have a CFW!
Mocha should never be used by end users, unless you need a real time debugger and memory manipulation tool.
But you know what, I just remember I did accidentally ran Mocha CFW FAT32 version last night too. I don't know if that has something to do with it.
Mocha is a temporary firmware patcher, when you reboot the console it cleans and removes the patches from memory.
using Mocha beta instead of Mocha not beta (other than being not a good idea to use Mocha at all) :
1) is useless because you don't need FAT32 support and
2) shouldn't have any effect on your USB drive's content. if you had a FAT32 partition with a specific folder on it, that folder would have been virtually mounted as "wiiu formatted drive".
you can't have that folder (because it's not FAT32) therefore it had no effect on your drive.
3) is worse because you lose USB access ! (that's the result of thinking latest == better ! without properly understanding the changes done in each version of a beta program)
Mocha version is BETA and unstable. So, maybe it's the cause of your problem. but the entire WiiU wouldn't be able to read its content, not just WUP installer.
That Mocha beta has a BIG bug : the USB port is seen as SD card port, the real SD card port is not seen anymore, the first USB drive plugged into USB is not seen as USB anymore but as SD card, the second not stealth USB drive is seen as first USB drive.
If you still use Mocha before installing a WiiU game, then "usb destination" is not available anymore, it's like "you don't have any USB connected". you have only internal and SD available.
Please, don't use Mocha anymore. NEVER.
if you don't have an installed CFW patcher (haxchi or CBHC) just use "simple signature patcher" homebrew instead.
but you said you have Haxchi already, so I really don't understand why you bother with complicated unnecessary dangerous and useless steps of patching CFW twice in a row?
If, even without launching Mocha, your USB is still not working with WUP installer, then I don't know why your HDD can't be recognized by WUP installer anymore.
did you search for that error number you get? (you linked someone with the SAME EXACT error, why not post in that other thread instead? it would have been a more similar issue than this thread)