It's not really that contrived. Plot-wise this was meant to send Domon West and show how the Pattern used everything at its disposal to place people where ta'veren needed them. Then in the long run Jordan meant to depict the Shadow as a vast web which escaped the control of the top servants of the DO very often, and where individuals were all competing against one another, hatching plots of their own for their own motives. At that point, Jordan was still at work introducing such plots without giving clues that they were not all the concerted work of the leaders of the Shadow - later on it became more evident that many plots were the actions of individuals. The plot against Domon wasn't meant to be seen through. Like many other things in the early books it was meant to shroud in mystery what Ishamael and Lanfear really were up to and how much control of everything the Forsaken had. In the prologue we had seen an Illianer woman who was a DF. That was enough to make us wonder if what happened to Domon was linked to the orders of Ishamael (most likely not, she probably got orders concerning the arrival of Rand in Illian with the Horn, should he come there). Followers of the Shadow are also shrouded in secrecy, so at the lower levels DF don't even know which other resources the Shadow really has in any given place. That happened early in TGH. The Forsaken beside Aginor, Balthamel (both dead) and Lanfear were released only after the second seal broke in Falme.
Domon has attracted the Shadow's attention after he bought a cuendillar disc from someone in Maradon who had no idea what it was. Rumors must have spread and DF tracked down Domon. What happened to him in Illian is either the result of direct orders from Ishamael to the leader of a DF circle to investigate Domon and retrieve what he had bought in Maradon (which the DF tried to carry out on his own as he could), or it was the result of a group of DF acting on their own, following rumors (gossip from the crew) that Domon had a collection of AOL objects (Ishamael collected OP objects, it's quite possible he rewarded DF leaders who managed to track down such for him).
Either way the Forsaken are very rarely "hands on", and unless it was confirmed he possessed a seal to the DO's prison (doubtful) he didn't warrant a plot in which Ishamael would get personally involved and would breach secrecy for (he didn't build such a complex hierarchy to breach its seccurity for every little plot. Ishamael wanted the DF to remain hidden until the very end, even if it forced his pawns to work much less efficiently).
That does not pass hard scrutiny though; it still amounts to the Shadow futilely pulling strings when it could have swung a hammer with far greater ease AND success. Occurring in TGH DOES make a difference for the reason you state (I recalled it as much later, around TSR or TFoH, but my last re-read was quite a while ago.) In general though, I think most people get too hung up on Machiavellian maneuvering, and that illustrating the foolishness of that is one of TWoTs major themes. Subtlety is great where it serves style and/or secrecy, but sometimes both are superfluous or even counterproductive, in which case subtlety is, too.
One could argue the Shadow did that from the start; had the DO simply ordered the surviving Forsaken to converge on Rand with thirteen Myrddraal during his first trip to the Stone there is little he, Moiraine and the rest could have done to stop it. It was a tactic apparently effective enough for Rand to fear during Egwenes trip through the testing ter'angreal, but not for the Shadow to use in mainline reality. Could have been an amusing exchange had everyone put their cards on the table.
Egwene: In the ter'angreal The Dragon Reborn begged me to kill him so the Shadow could not turn him, Sheriam Sedai.
Sheriam: Do not be foolish, child; we are far too wise to achieve final eternal victory so effortlessly.
Or consider the eloquent little Darkfriend oath to remain faithful UNTIL "the last hour of my life" that let Verin infiltrate their order with the sole and quite successful goal of exposing every last one of them by name. With all the rules-lawyering and prevarication Aes Sedai honed to their own subtle little art form over three millennia one would think at SOME point Ishy would have the presence of mind to say, "y'know what? Just swear to serve the GL faithfully FOREVER, period." Sometimes people outsmart themselves, which is all the plot against Domon was ultimately meant to demonstrate anyway: Good will always win because Evil is stupidER. 
Last First in wotmania Chat
Slightly better than chocolate.
Love still can't be coerced.
Please Don't Eat the Newbies!
LoL. Be well, RAFOlk.
