What I am about to discuss is purely speculative. I cannot prove it. But I can argue for it. If there are so far no theories out there as to how the Trojans diverted the Scamander river, at least there is one now.
"Where the winter stream of the Bunarbashi-Su joins the Mendere, there are some immense blocks of irregular shape; they may have formed part of the wall of a small fortress" (Dr Peter Forschhammer, Topography of the Plain of Troy, p 39).
Forschhammer, who visited the plain of Troy in 1844, tells us that he saw large blocks in the area he calls the winter channel of the Burnarbashi Su, which is a place in front of Pinarbasi where the western most rivulet in the plain can discharge eastward into the bed of the main river in the center of the plain. That western rivulet is today known as the Pinarbasi Su.
In the map above by Thomas Spratt, the Winter Channel of the Bounarbashi Su appears between the T and the R in Troy. That position is just a little down stream from the large eastward loop that goes around the top most anomaly pictured below.
In the above photo, there are two raised earth anomalies across from one another, with a canal and road between them. Forschhammer saw the blocks in the area near the left edge of the lower most anomaly.
Forschhammer suggests the blocks could be the remains of a small fortress, but that fort would have been in the middle of a flood plain, and would not have survived for long. I think it is more likely that what Forschhammer saw were remains from a dam. I suspect that what we are looking at in the above photo is 3000 years worth of mud covering two parts of a failed dam. The dam is under 5-7 meters of alluvium. Imagine a two story deep carpet covering the bronze age surfaces and structures.
Zangger tells us that determining the age of the canal cut into the bedrock at Besik Bay "has never been seriously attempted, although Schliemann argued plausibly that the canal must have been very ancient, because it had accumulated a beach at its mouth in Besik Bay, 1 1/2 square miles in size, and it could not have done so in just a few centuries" (The Flood From Heaven, 1992, 145). In addition, the alluvium in Besik Bay does not come from the springs at Pinarbasi, it comes from the Scamander river, which runs in the center of the plain.
It follows that the Trojans must have diverted the Scamander out of the plain and into the artificial channel at Besik Bay. That is the only way the beach at Besik Bay could have been formed.
How did they do it?
If there was a dam below Pinarbasi, it would have created a reservoir behind it. If that reservoir was allowed to flow off to the western side of the plain, it would have put the river water into the pre-existing channel of the Pinarbasi Su, running down the western side of the plain.
So, I propose that the redirection (or partial redirection) of the Scamander/Mendere was achieved by damming the river, and letting its reservoir flow off in a new direction.
In the diagram above, the yellow arrow points to an area where the reservoir of the Mendere flows off into the channel of the Pinarbasi Su. The light blue line represents the dam. The yellow circles mark the citadel and the greater city of Troy. Blue dots represent reservoirs.
So, how did the Trojans divert the Scamander river? They dammed it to form a reservoir which they allowed to flow out into the Pinarbasi Su. Some or all of this water then made its way to Besik Bay, at the bottom of this photo, via the channel cut into the bedrock that is still there today.
The dam must have lasted for a long time to have created such a large beach at Besik Bay. If it was built during the era of Troy II and lasted until around the time of Troy VI or VII, it would have had perhaps1400 years to build up the beach (2600 -1200 bce).