The Masamune may well have moved on its own volition, even if it was present in the original timeline in the Ocean Place. We see that Masa and Mune are able to move it (such as when it powers up at Cyrus' grave), and we see that the Pendant is also capable of locomotion. The same can't be said of the Mammon Machine. However, if those dreamstone objects could move, I suppose the Mammom Machine could as well, which might explain how the FF would have gotten outside the Ocean Palace ruins (but that would then require the MM to also disgorge the FF, so it couldn't be found inside that lovely artifact which would have merited mention and study).
While the FF is a powerful artifact, other than opening itself, there is no evidence to suggest it is capable of movement. Indeed, the fact that is stayed locked in Chronopolis for several thousand years, and later it is left on Terra Tower, seems to indicate it relies on the kindness of strangers. It would seem that the masamune (and possibly the pendant) are capable of motion because of the dream creatures that inhabit it; the FF lacks such special circumstances.
Of course, the evidence linking the Red Knife to the Ocean Palace on the original timeline is merely that we see that the Red Knife is different than the Masamune. If it had to be powered up in the CT timeline, one would assume a similar level of powering up in the original timeline. However, I would argue that the Red Knife would not have been used against the Mammom Machine in the original timeline for the simple reason of that reeks of predetermination, which the games appear to not be in favor of. Also, in the flashbacks, the Mammon Machine seems to be whole and lacking those wonderful lightning effects that occur when the red knife is thrust into it. And if the Red Knife was present in the original timeline, and the Red Knife (like in the CT timeline) came before and potentially caused Lavos to awaken, why did Magus leave it with Melchior?
Which is all a fancy way of saying that the Masamune/Red Knife probably wasn't in the Ocean Palace.
Though as a counterpoint, the MM being sent to the DBT has always been incredibly random with no good reason presented; the games are quite capable of doing things that don't make much sense.
As for the destruction of the Black Omen, being in the center of a debris field is hardly better than being inside of a ruin, though it would at least then be possible to discover it without the husk of the ocean palace getting in the way.
But for the MM being spat back out? That is really stretching things. It would be easier to say that Schala was still around at that point and the MM was sucked into the vortex along with her after the MM was defeated (though that then does bring up the question of where Schala is while the party battles it). Or it would also be easier to say that the Schala and MM that were sent to the DBT were from a time period other than the one in which the Black Omen rose (but that would make the MM in the Black Omen a Time Bastard, I believe).
