Well an update for anyone else who comes across this and has the same problem as me - I spoke to Google support, HTC support and O2 support about it. None of them seemed to have any real idea how to fix the Nougat update problem, nor how to get the phone working again with Google apps from Android 6.0.0 after the factory reset.
Google support seemed the most interested out of all three, especially in the factory reset problems and seemed to acknowledge that there seemed to be a problem with the way the Google apps weren't working from the factory reset (especially that Google Play Services was completely missing from the factory reset apps). But they weren't "able" to offer any further support in my case because the Google Play Services app was missing and they can't support third party installs (downloading and installing it manually) in case that leads to further problems down the line. So because it was a HTC phone rather than Google phone, they then told me I had to take it through HTC despite it being Google apps (and their Nougat update attempt) causing the problem.
HTC were also more helpful than O2. O2 typically passed me through three different people in the online chat (HTC and Google only one person) and despite saying they'd read the chat from the previous two people, the third at O2 continued to ask obvious questions like have you tried making sure there's enough internal storage available for the updates? Well, you'd think a factory reset might just free up enough internal storage seeing as it wipes all data from the internal storage, right? That was the moment I facepalmed.
I'm reluctantly having to send the phone in for diagnostics and repair (first time I've ever had to), but both O2 and HTC offered to take it in (O2 via Carphone Warehouse), so I am going for HTC directly. I hope this doesn't happen to anyone else but maybe this will be helpful if it does.
