Don't overthink it. Time is what clocks measure, just as rulers measure space or distance.You never hear people asking "What is the ontology of distance?" it's a parameter that can be measured with clocks, nothing more. It is existential with space and does not require objects for it to exist. What objects do is curve spacetime and thus alters the rate of time relative to another frame that is not moving with the same velocity and/or not in the same gravitational potential.
See my response to Thoram. That's as much i think I know on the subject.
I think the notion of the soul arises from Cartesian duality which stems from religion; the mind and body being distinct. The evidence suggests, as you know, that mind (soul) is an emergent property of the brain's processes.
So we are back to the question as to what empirical evidence we have for the "soul" and whether we can make predictions about it, or measure it, or whatever.