But I pushed it forward 10 minutes and it does [b]stall the 'loading' of the page[/b].
Yes , me too like your 2nd screen , loading , loading , loading 1 day long but never reach my account.
Then there is the inconsistency if it is only happening on one of your systems.
it happens on my 3 differents OS (Wxp,W7 and w8) , definitely a black cat in my house :-[
Why I have no idea, but I still can't see why anyone would be running (or need to be) with the system advanced. Resetting my system time allows the page to load.
It is not a question of needing to advance the watch, but more if the time of the system takes the lead step by step. I know quite a system where the clock is not necessarily synchronized on the internet time. In my case, it takes only 1 minute in advance since a long time , sufficient to prevent my account to open Now, sorry if I was wrong and you can fully enter your account (not just as in your image showing the loading)

However it is true that the clock has more chance of delaying days after days than advancing.
Everything worked on my other 2 systems that had no advance before I decided to force them.
Not by need, but to check what seems to me to be an evolution of firefox with respect to time.
With firefox 49, I can put 10 hours in advance, it does not pose problems opening my account , with 50 , 51 , 52 it does.