You haven't provided any evidence to refute the time and distance answer.

Be'lal not being transmigrated bolsters my answer.

RJ indicated that if the amount of balefire is small enough, then the Dark One can still save a soul. The only known effect of smaller versus larger balefire, is the amount of time that is erased from a thread's existence. The smaller the balefire, the less time, and vica versa.

This is direct evidence that it isn't balefire in itself that prevents transmigration, but the fact that it reduces the Dark One's window of opportunity.

Next, it is entirly logical that the Dark One's influence is stronger the closer you get to Shayol Ghul. For example, the Dark One can feel instantly if someone embraces the Source at Shayol Ghul, as indicated by Demandred. So it is logical to suggest that the Dark One would be able to grab your soul quicker if you are standing on the slopes of Shayol Ghul itself, than if you are standing on the Isle of the Madmen, 10 000 miles away.

So, the Be'lal incident clearly shows that the small amount of balefire used by Moiraine made it impossible for the Dark One to save Be'lal. Yet it is difficult to see how you can make a smaller amount of usable balefire than the finger thin bolt produced by Moiraine.

This indicates that the Dark One WOULD be able to save someone from such a small amount of balefire (as stated by RJ), if other circumstances were different.

What circumstances could these be? Why, if the victim was closer to Shayol Ghul of course. Tear is very far from Shayol Ghul.
Andor is closer, but it seems still too far away, since he was still unable to save Asmodean from a very small amount of balefire.

Asmo didn't die in a Stedding. There is nothing special about the place he died. The only relevence the LOCATION of his death could have in this context, is the distance it is from Shayol Ghul.