I'm not sure this is an answer, but it's too long for a comment.
How do you expect to freeze the pykrete?
If you simply expect to dump all this material (stated by other answers) and it freeze on it's own, you are adding to the problem of rising temperatures. Even if the water and wood mixture freezes, it has raised the surrounding temperature to do so. A single ton of this material probably wouldn't make that much of a temperature difference, but at the amounts you are talking about, you're likely to cause more problems.
The Second Law of Thermodynamics tells us:
2. When heat is transferred from one body to another, the temperatures equalize. As the temperature of the heat source falls, that of the heat sink rises.
So, as the water and wood mass loses temperature (heat source), the temperature of the surrounding ice (heat sink) rises. Of course, this doesn't account for latent heat, but it's still heat transfer.
Cooling/freezing materials in a mechanical way, such as using a refrigeration unit, simply moves the heat from one material and radiates it in another location. Needing to freeze X,XXX number of tons of water and wood will raise the temperature of another location by a considerable amount.
The First Law of Thermodynamics tells us:
The internal energy of a system is constant unless changed by doing work or by heating
So, we would have to move the heat out of the "system" of the poles and move it someplace else. Unfortunately, on a scale this large, the Earth's atmosphere likely becomes the new "system". Unless we radiate the heat directly into space, we're simply robbing Peter to pay Paul.
To do any of this freezing in a man-made way would take massive refrigeration units that would cause more heat production and greenhouse gasses, causing more issues with the heating of the poles. Even if we could physically build them, the cost would be astronomical, probably on the order of the GDP of some medium sized countries.
And if would could still manage that, why not go ahead and just freeze salt water? It freezes at about 28 degrees F (https://oceanservice.noaa.gov/facts/oceanfreeze.html) and we'd have to get the ice to be considerably colder than that to stay frozen for any significant amount of time to make the effort worth doing.
According to an article I just found, the ice is also melting from the bottom:
With global warming, both of the poles are warming quite quickly, and this warming is causing ice to melt in both regions. When we think of ice melting, we may think of it melting from above, as the ice is heated from the air, from sunlight, or from infrared energy from the atmosphere. But in truth, a lot of the melting comes from below. For instance, in the Antarctic, the ice shelves extend from the land out over the water. The bottom of the ice shelf is exposed to the ocean. If the ocean warms up, it can melt the underside of the shelf and cause it to thin or break off into the ocean.
The research paper the article references:
Using a simple ocean model driven by observed forcing, we show that freshwater input from basal melt of ice shelves partially offsets the salt flux by sea ice formation in polynyas found in both regions, preventing full-depth convection and formation of DSW (Dense Shelf Water).
Instead of just dumping ice on top, the real answer seems to be to also remove the heat from below. So, to make our ice in a manner that might work, we would have to take at least some of those ginormous refrigeration units to the bottom of the ice shelf to cool the bottom of the glaciers.
Now that I've written this out, it seems more like an argument that the real scientists in your book would use against the "eccentric world leader". Combine this answer with the other answers provided, and the pykrete plan really does seem to be a horribly thought out plan, just like you might expect from a politician who gets their "good ideas" from lobbyists.