Between my friends and I, we have seen this problem not once, but FIVE separate times with Elite and the XB1.
In all cases ED seemed to be the cause. It was ALWAYS the first game (and in some cases the Only game) to exhibit problems. Possibly due to how hot it runs the xbox. If you mesure the temps on your xbox, you will see elite tends to run the XB1 considerably hotter than most other games.
In all 5 cases a reinstall was tried then a factory reset. In all 5 cases, only a new XB1 fixed the problem. I have also talked to lots of others online, all with similar stories
This may or may not be your issue but it seems to be pretty common so you should consider it. 8 out of 10 people i talked to who have had to replace an XB1 in the last year have been heavy ED players.
Is this just a coincidence? Or is it a pattern? Either way, this is why i always put the extended warranty on consoles. I have already had to replace a PS4 and TWO XB1's.