I've been catching hell from the Quantum Qiddies who inhabit Philosophy SE for answering similar questions; let's hope they're about as creative as they appear and therefore don't come to this site. :)
That said; there's no such thing as 'meta-time'. There's no sense of time outside time that a human could perceive, and there's a very simple (though not easy) reason for that - the second law of thermodynamics.
The Law of Entropy is the ONLY law we currently have (for classical physics at least) that can only operate in one direction in time. It states that in any closed system, 'chaos' increases over time. Chaos in this case has a very special interpretation, and you should think of it as the number of possible internally ordered states that can describe the system state.
Another way of putting that is that the universe tends to even out localised variances from an equilibrium state.
In the human brain, that means that in order to remember something, the brain lays down a higher local order in the brain (to store and organise the memory) at the expense of lower global order (by expelling a relatively massive amount of heat). This is why wearing a beanie in the snow is so effective; more than 20% of our body heat is radiated through our heads.
It also means that we can only EVER remember in one direction of time, into the past. Further, it means that if we ever exist out of time, there is no entropy occurring, meaning that there is no perception of time, no memories being recorded; no meta-time (or time of time).
How would time travel work? In theory, our progression of memories would be subjective; we could remember our individual timeline and so long as we don't go somewhere that doesn't have entropy occuring, we'd remember all that we currently remember, and continue to remember from that point the things we observe in the new point in time. There is much to discuss on this point but it's out of scope for this answer. The important aspect of this is this;
1) We can't foresee the future but we can predict it because at the classical scale at least, physics seems to follow deterministic rules.
2) We can't function as we do now in a 'timeless' state as the best that can happen is that we would go into a form of stasis, not able to function in any way.
All things considered, the problem your precogs face is getting around Entropy, and I can sincerely say to them 'Good luck with that'.