Assume, say, an ordinary, fairly complete description of your actions today, written tomorrow. (It will be our "functionally omniscient" object when it starts time-travelling backwards.)
Assume now, that through some cunning artifice that tale of events is moved into yesterday--but you don't know about it.
Your day carries on the same way that the tale outlines it--but it would be a stretch of logic to say that these words on paper "remove" your free will. Had you done something different, that something different would be in the tale instead--one might even say that your free will changed your unknown "destiny".
For a slightly modified case: Assume instead that the tale of today's events was read to you this morning, and you had thought about it and planned your actions accordingly. This would be weird. Regardless of this, however, the contents of the tale read to you are determined by your actions today, which in this case are determined by the contents of the tale, which are determined by your actions... It creates an infinite loop, the outcome of which would be undefined by logic as we know it. One might use it as a disproof of the possibility of knowledge of the future happening; another might use it as a disproof of the possibility of free will.
Aside:(What would your destiny look like when you saw it? I think it might well be illegible, or at least produce very odd results--although on the off chance that it actually worked, you could not fail to be happy with your destiny because of the infinite amount of time you spent in its redefinition.
Anyway, free will and omniscience are therefore volatile and possibly contradictory, but only when they interact--which is probably why "true" prophecies are both rare and obscure enough to not usually be decipherable until after the fact.
This is a thought I have very clear in my head and any grievous mistakes in this writeup are probably due to verbalization error. Let me know.