That there are two ways to enter TAR, either in the sleep or in the flesh. From Hopper we learn that Slayer enters TAR in the flesh due to the DO's powers. Since Luc and Isam are the same person, this person enters TAR in the flesh. There is nothing to support your idea at this time that Luc was basically a Dreamwalker, but Isam's ghost (?) was in TAR "in the flesh". And again, your idea was proven wrong, but you still insist that everybody should have come up with your explanation, how Slayer uses TAR.

There are also other hints, for example it's said in TSR that Fain's Myrddraal fears that Isam might "find" him. This suggests as well that Slayer's job is to hunt, find and kill renegades of the Shadow, apparently using TAR in the flesh to travel (since Myrddraal don't dream).

Besides that, as I pointed out, it's certainly possible to link Slayer to the murder of the BA in TSR (the book where Slayer was introduced as a character), because he is obviously a assassin resource of the Shadow better than a normal Gray Man, as Moiraine puts it. And then you could also deduce that he likely killed the Gray Man in the WT as well.