Before our troops supplies run out, the High Seas Fleets would send further reinforcements, including more subs. Such a fleet would be directed into the western sea to push back the enemy ships who have attempts to cut of part of the task force, while submarines countine targeting enemy ships in "Wolf Packs." To break out of the desert the large invasion force would March southwards in a blitzkrieg like offensive, with a strong rear defense to reach the more fertile regions of the south (as not the entire island would be desert.) After the push back, supplies would be dropped off at the other coastline, where a small number of troops would be waiting, the supplies would then be brought back to the main force.
"A desert is only a prison if you can break out of it!" - Major General Javius Laskarion, 1 AEF.