You say that you thought something about Slayer back then, which was simply wrong, and consider that no one could figure the right thing out, although the clues are there.

Personally, I think after what we learned about Slayer in the first books, especially in TSR, it was possible to figure out that he killed the BA in the Stone (Moiraine even tells about that murder: “I doubt even Gray Men could have managed that [...] the Shadow has resources beyond what we know, it seems”; and just a bit later we see such another assassin resource) and the Gray Man in the WT. And if one manages that deduction, it's only one further step to conclude that he is the obvious suspect for Asmo's murder as well.

But maybe you are one of those slow of wits, who RJ mentioned when he talked about Asmo's murder:
"It seemed to me that there was no need to go into any more detail. I thought that if I went into any more detail, I was being blatantly obvious, and you know... what do I need to do? Caper around with a sign saying 'Here! Here! There he is, see?' I mean.., I assumed that the people who read my books are intelligent to a certain degree, have a reasonable level of intelligence, and are able to deduce things that you know... I mean, I don't have to tell them water is wet. They know that. I don't have to tell them that if they fall of the roof, it's gonna hurt when they hit, you know, they know that. So I... no, I... At this point, I must tell you: although I will continue to put clues into the books. Again. A bit here and there. If I see a spot where I can put a clue, for those who are slow of wits to catch up".

Like water is wet, it is simply obvious that Slayer, as a top assassin or bounty hunter of the Shadow (and IMO one could deduce Slayer's profession from the books before LoC with a reasonable level of intelligence), whom we saw hunting & kill renegades before in the books, killed Asmo as well.