Interesting reading your above post....a pity from my point of view as only yesterday I returned my Pro 4 to be "repaired"Like you said it's complicated... here's the knife in the back... because it came with 8.1 you can only download an 8.1 Recovery Image (dear MS please change this) so Id recommend using the W10 Media Creation Tool downloading the Windows 10 installation image and the Surface firmware & driver pack. Then you can wipe the disk on your Surface and install Windows 10 and update it. Oh wait... did Windows 10 ever activate on your Surface? if it did then there's no worries. If it didn't ever activate then it's more complicated...
use that Dubai shore time to get you a working entertainment system
Booting was impossible...could open EUFI but nothing worked....downloaded on another computer the W10 Media Creation Tool and chose "for a different computer".
Copied to a USB stick and inserted in Pro4....this informed no Drivers available.....so came to a full stop not knowing there was a Surface firmware & Driver pack.
To add to my knowledge would installing the above pack have allowed me access to the SP4.... in order to wipe the disk and then install the ISO?