I’ll have a go at this in the meantime 
“You have all the time in the universe” is referring specifically to one’s experience as a flesh and blood body only, one exists where time has no duration. It is impossible to ever ‘run out of time’ as time does not move in actuality.
Whereas as an identity ‘I’ am locked out of eternal time and instead ‘I’ exist precariously across the past, present and future. This is where ‘I’ am always managing, anticipating and running out of time.
As it is always this moment, this body does not move through time like the identity moves across the past, present and future. Rather this body exists securely in eternal time.
In eternal time there is no distance to be travelled between ‘then’ and ‘now’ as the immediate is the ultimate, whereas ‘I’ am forever shifting between these thin slivers of ‘real time’, desperately trying to hold, manage and anticipate each one.
I think I have just answered in part my own question - of why is it that where time has no duration there is such safety. Because all this painful psychological/psychic activity which comes from ‘managing time’ (whilst being forever locked out of actual time) ceases when one exists in eternal time. Everything is in it’s place already as one is not actually going anywhere or coming from somewhere.