Pykrete was never going to be used anywhere near the Mediterranean, so didn't need to resist the heat of the equatorial sun.
It was intended for use, primarily, in the northern Atlantic. The "berg ships" would have basically been floating runways for military aircraft, and no-one in WWII was launching aircraft from the Mediterranean sea.
Pykrete was made from wood shavings or sawdust and water, not wood pulp. Wood pulp is much finer, so provides much less stability to the structure, as Adam and Jamie showed.
Since the point of pykrete was to use cheap, readily available materials, something that had to be manufactured; wood pulp, wasn't even suggested at the time. Whereas wood shavings and sawdust, are common by-products.
Jamie "improves" the pykrete design using hundreds of newspapers, which were in short supply during the war, so not a viable option.