This is already a better idea than a Forsaken who didn't know Asmodean was shielded commissioning Slayer to kill him (and that Slayer wouldn't be so afraid of having to face a Forsaken that he wouldn't do it while his target was asleep), and beside I'm pretty convinced aside from Ishamael it's Lanfear who likes to use Slayer's services so much - she believes TAR and everyhting that roams it is hers, after all. I'm sure it's her who sent him to kill the greymen Ishamael sent to kill Egwene and Nynaeve as she intended to use them and Mat and she "saved" Perrin from ishamael in TAR in the same book; I'm fairly certain it's her who ordered Slayer to kill the two BA in Tear and make it appear it was clearly retribution for revealing secrets (when in fact, the BA are bound against betraying the DO). Elayne puzzled out that was the real motive of those executions: to convince them what the BA revealed was valuable information and thus send them hunting based on that information, and away from Rand. It's Lanfear who had a motive to clear Rand's entourage a bit, especially the "distractions" like the girls, before the new phase of her plans began. And she was constrained to do so without harming them, or Rand would have suspected her right away, and her plans were in ruins). I suspect it could be Cyndane who tried to have Slayer kill Rand and Min in WH as well, especially because Min was included in the orders - but that is less certain and could well be Aran'gar, or Demandred (but I don't trust Slayer's certainty that it was a man, I think he said that because of the voice, not because of any special power to tell saidin from saidar). Finally, I suspect Slayer may have killed Barthanes at Lanfear's orders in TGH, because in the end it's Fain and her who had motives to impede/distract Ishamael)

However, your idea doesn't work well. Lanfear didn't hate Asmodean, she merely despised him. She had no good motive to make a contingency plan for Asmodean to die if she did, beside using this as additional pressure on Asmodean's loyaty, in which case she would have had to tell him if anything happened to her he would die. Lanfear is totally selfish. Like all the others, she's hardly the type to care what happens to the world and other people after they died. If she's no longer around, Shai'tan can rot in his prison forever, for all she cares. If she made a contingency plan, it would have been to get Rand killed if she died (the "if I won't have him, nobody ever will" logic), not Asmodean or anyone else, but I don't really think she cared, or would even envision her possible demise.

Your logic about balefire is flawed: we know as hard fact that when a small amount of balefire is used, it only makes it harder for the DO to seize a soul, because the window of opportunity is much smaller. Balefire in itself can't always be the sole factor preventing the DO from seizing a soul, not if a small amount is used, and the potential killer would have three very good reasons to use a minimal amount: 1. a big amount wasn't necessary, even the smallest amount of balefire kills; 2. to avoid detection if possible. 3. the killer couldn't know what Asmodean (or anyone bumping into them) was doing even minutes ago and what sort of alarm he/she could trigger in the palace by erasing more of Asmodean's life than strictly necessary. For all he killer knew, Rand or another channeller could be two rooms away and have interacted with Asmodean minutes ago.

If a channeller killed Asmodean, balefire was the most logical choice, as it's the only thing Asmodean couldn't parry in any way, and the killer couldn't afford this to turn to a duel (and let's remember only Lanfear, Moiraine and Rand knew Asmodean was "diminished". The killer was in enemy territory, and it's not impossible he/she even had that weave ready - not for Asmodean specifically but for anyone who bumped into them.

As for the "where" factor, it may well be distance from Shayol Ghul (ie: Shai'tan may have to find his way in the Pattern to the soul, and the more distant from SG, the more time it takes). Jordan may have expected us to infer it from Be'lal's death, and from the blatant evidence that the closer to SG, the greater the DO's influence on the Pattern is. He wasn't brought back, even though Moiraine believed she could remove only very little time with her balefire. It sounds like the window of opportunity is really quite small, and every second may count.