Omniscience?

"...he did not know the future. Nor, he believed, did the gods. (Well, the branching universes are so many, and each so strange, that probably none but the One God can keep track of them.)"
-Poul Anderson, Operation Luna (New York, 2000), p. 283.

There are philosophical problems with the concept of omniscience. Apparently, Godel has proved that omniscience is impossible. I do not know his argument but here is mine:

if everything were known, then nothing would be unknown;
if nothing were unknown, then nothing would be future;
if nothing were future, then everything would be past or present;
if everything were past or present, then, at the next moment, everything would be past;
if everything were past, then everyone would be dead;
if everyone were dead, then nothing would be known;
thus, if everything were known, the nothing would be known;
reductio ad absurdum;
therefore, it is not possible that everything is known.

(I think that) any consciousness requires a remembered past, an immediate present and an unknown future. Atemporal consciousness - a single instant of durationless sensation without memory or future - would begin and end simultaneously and thus would not exist. Another reductio ad absurdum.

It may be argued that omniscience is knowledge of everything that exists and that the future does not yet exist. However:

we usually include the future among the things that are unknown to us but that would be known to omniscience;
it is convenient for some purposes to regard all moments as coexistent even though we are conscious of each moment only in that moment;
simultaneity is relative in relativity theory.

Omniscience would have to be neither temporal nor atemporal but transtemporal, incorporating and transcending instead of negating duration, but is that possible?