OK, so I wanted to come back and re-visit this since Hark and GMG became involved, so that anyone who searches and comes across this thread knows that there was a happy ending.
Once I had proved the issues to Tim at Hark, he arranged for one of GMG's support guys to call me. Spent some time on the phone with the support guy, at the end of which he agreed that the controllers were most likely faulty.
Tim then arranged to express freight a replacement controller that had the latest firmware already installed on it. He also threw in a bag of pellets, a GMG hat, and a replacement igniter rod (presumably because one of the tests we did might have damaged it or shortened its life somehow.
It all arrived the following day and I put the controller in straight away, checked firmware, and immediately attempted to do a firmware update using my phone's hotspot. Holy crap it worked. Tried it again on my home network - it worked again. Went through all the issues I was having between all controllers, and this controller did not have any of those issues.
In summary; this issue was NOT an issue with my iPhone, home network, or anything in my control. It was a case of 3 faulty controllers. To be fair, Hark and GMG have never seen this before (the faulty controllers are going back to GMG in USA to work out what went wrong). Despite this, the way they responded when they became aware of the issue is to be commended (i.e. they didnt once blame me or my equipment for the problem). In discussions with Hark and GMG, I actually asked them about some of the possible issues that were suggested in this thread, such as using Android instead of iPhone, Apple not updating wifi protocols or having old wifi protocols on devices (requiring complete wipe of phone), etc. I was advised that none of these issues are current or relevant to their product - in fact I had wasted time in procuring an Android phone to prove without doubt that it wasn't an Apple issue.
My issues with regard to the GMG app were also resolved in this week's update, and it appears to function exactly as documented now.
The lesson I have learnt out of all of this, is that the forum as a collective is great when it has seen a particular issue in the past, however when issues present that have not been seen by the collective, or the solutions are not working, it is best to go back to the manufacturer for resolution (I probably should have done this sooner to be honest).
Finally, during this whole ordeal, I did actually spit the dummy with this unit before Hark and GMG got involved. As a result, I tracked down and put in a pre-order for a Yoder YS640 with competition cart and grill grates. The GMG will probably either be my second pellet grill, or it will end up going to my mum's once the Yoder arrives (she was going to take my WSM, but she can have this one instead).
So all in all, happy story in the end. The GMG was a cheap way to get me to experience the concept of pellet grills (even in its manual mode without the technology working, it confirmed for me that its the way I wanted to go), and for that I am grateful, as I might not have made the jump to the Yoder otherwise.
Just have to give a big thank-you to Tim Harkin and GMG who were professional and courteous at all times, despite my frustration which was probably not expressed particularly well and my ADHD/autistic tendencies which dont make me respond well on a good day most of the time.