On reflection, it doesn't even matter whether Obliviates and FMCs are normally removable in this universe - Harry would use a delay in carrying out sentence to either attempt to find a counterspell or find the real perpetrator or both.

This is a good point; agreed.

So no matter what, for Harry, a one-year delay in carrying out sentence has a really good cost/benefit tradeoff.

I would have said a one-week delay.

And if Dumbledore won't exert himself sufficiently to secure that

I see no reason to think that Dumbledore is even remotely capable of that. Politically, Lucius and Dumbledore are near-evenly matched, and Lucius is presumably willing to exert all his influence on his end of the trial. Even assuming Dumbledore calls in every favor he's owed, I don't see that it would accomplish anything but get the situation to default to normal procedure- which is what's happening now.