Ship to shore enhanced. Introducing the hover barge.

Concept.
via Columbia Helicopters...

In June 1982, Columbia Helicopters was hired by Sohio to participate in a test on Alaska's North Slope. The purpose of this test was to evaluate the ability of a helicopter - the Boeing Vertol 107-II - to tow a fully-loaded hover barge over water, snow and ice.
The test began in Prudhoe Bay on June 17. The Vertol's 600-foot long line was connected to hover barge ACT-100, jointly owned by Global Marine Development and VECO. Air blowers on the 170-ton barge forced a cushion of air under the barge, which was kept in place by rubberized skirt material.
This first test was run around Prudhoe Bay with an empty barge, and was successful. During this and subsequent tests, the aircraft often flew with a nose-down angle approaching 25 degrees. Next, ACT-100 was loaded with 40 tons of cargo for another close-in test run. Once more, the helicopter showed it could move the barge despite the additional weight. The final aspect of the test was to tow the hover barge over a 50-mile course to a drill site named Alaska Island where Sohio had just completed an oil well.
During the tow to the island, headwinds over 30 knots were encountered, and snow and ice buildup were also factors. Regardless, the Vertol was able to bring the empty barge to the island successfully. On the return trip to Prudhoe Bay, when this photo was taken, the barge carried 50 tons of cargo, bringing the total weight to 220 tons. As with the previous tests, this task was accomplished successfully.
This photograph is one of longtime Columbia Helicopters' photographer Ted Veal's most famous photographs. The use of a powerful telephoto lens makes it appear as though the helicopter is closer to the ice than is actually the case.
Hover Barge Tow Photo © Columbia Helicopters, Inc. 1982

It would have to be tweaked for military use, but hover barges have been in use by the commercial industry for a number of years.  If towing a barge with a CH-53 (even if you're more than quadrupling its normal payload) doesn't make sense militarily then how about this system from Hovertrans from Singapore.

Basically it takes an LCAC (in military terms) and has it act as a tow ship to four 50 ton barges.  One trip ashore and you have moved 200 tons instead of 50 or 60.

Ship to shore can be solved.  Oh and you're asking how do we transport these "extra" hover barges to theaters?  Easy.  They're with the follow on echelon aboard the MPF ships.  Besides the added benefit of being able to discharge cargo directly across the beach...without the need for port facilities (think Haiti if disaster relief is your primary motivation).