Unable to change Gamertag via Web or Console

For the past 6 days I have been attempting to change my Gamertag on an account that I've had since 2006... but regardless of trying on multiple browsers/machines and even on my Xbox console, the gamertag does NOT change. I haven't changed my GT since the new system was introduced a few years ago, so have a 'Free Change' available.

When I go to https://social.xbox.com/changegamertag, I get a message that says:

"Since this is your first gamertag change with the new system, we are giving you a freebie. But after that, you may have to pay for it.

1. I enter the unique username in the Your New Gamertag field (eg: XboxOne) and hit Check Availability
   
2. The next screen shows XboxOne is unique & available (without a suffix). I click the option that says Confirm Gamertag Change
   
3. I get a popup box that asks for final confirmation that I want to change as I won't be able to change back, and I select Change Gamertag.
   
   (Note: 'XboxOne' is used as an example only and is not what I am trying to change it to)
   

Nothing happens after I've done this. The screen does not show any sort of confirmation message, and the pop-up box remains on screen yet my Gamertag remains as it was. I can press the Confirm button repeatedly and nothing happens. I refresh the page to try again:

1. I still have the same statement about this being the first change with the new system, so it shows that my previous request had not completed properly. I re-enter the unique username in the Your New Gamertag field and hit Check Availability.
   
2. This time, the username does not show as unique and now has a suffix after it (eg: XboxOne3133).
   
3. I do not confirm the change, as I want the gamertag without a suffix.
   
4. If I return back 30 minutes later and try the entire process again, the Gamertag goes back to showing XboxOne (without the suffix) so I assume the GT is reserved for a short period until the process completes (which it never does).
   

I have tried this on 3 different machines with 3 different browsers (9 separate sessions) multiple times and via my mobile phone -- all give the exact same result.

If I try to do the change on my Xbox via the Profile customisation screen, I get a similar issue - except this time I get an error that says "Sorry, something went wrong. Please try and change your Gamertag again" with no other information. The rest of the process mirrors the above.

I called Microsoft support who confirmed that the Gamertag I was trying to claim was 100% unique and unclaimed and that there were no issues with it being a banned phrase (etc), but cut me off when I trying to delve in to what the issue was. I requested a call back via the Help Page 3 further times (getting cut off each time with no attempt from them to re-establish the call) and cannot request another call back as 'You have reached the limit for a call back, try again tomorrow' despite not receiving an answer to my question.

It was Microsoft who dropped the call all 4 times as my phone tells me when the other person has hung up - very poor customer service, so I am forced to write it here for a resolution. What stings is the last agent I spoke to, I told them I kept getting cut off and she promised to call me back if it happened on that call... of course, she didn't bother. Can anyone give me some advice on what to do other than speaking to Microsoft Support again, who have been as useful as a chocolate teapot in all honesty.

Additional Information

• I first attempted to change my GT on Monday 27th February. The problem has continued since then.
  
• Xbox Live status shows GREEN on the Gamertags subsection, stating everything is operational.
  
• I have tried this process on Edge x3, Firefox x2, Opera x1, Chrome x2 & Safari x1 across 3 separate machines to rule out a dodgy browser session.
  
• I have logged out of my account and back in on all devices. All sessions show my existing Gamertag, and not the one I am trying to change to
  
• I have tried to do this via my Mobile Browser via a cellular network to rule out an issue with my home network (admittedly clutching at straws here).
  

I appreciate any and all replies, but have tried to give as much detailed information as possible to limit any generic responses asking me to 'reset my console' etc as I have seen on similar posts. This appears to be a problem on Microsoft's end rather than on mine and I would really appreciate some help with this.

:)