The other sandbagging will have to be done by the British, specifically Egypt and Yunnan or where ever you draw the line in China.
As to nibbling the edges, I am calling this Operation Ricochet. The Axis flood rises high. Many areas might be covered. Hopefully temporarily. For the enemy to reach the Middle East is no easy feat. With proper maintenance and investment, it should be an excellent area to begin taking back. For America’s part, parking a fleet next to Gibraltar can aid the English effort there by instilling a sense of fear in the Italians. A build or two will need be devoted to the potential defense of Rome. Those forces may never move for the rest of the game, nor be transported to North Africa nor can-open for Germany in the East. Meanwhile, you are free to choose from several edges where you might land: S. France, Greece, Yugoslavia, and Albania.
Scandinavia is another area that may be easily nibbled. Economically, it could be called a money peninsula, given the gain/loss of IPC and bonus income. It can even be the sight of an American minor complex.
If some of the sandbagged areas are lost, a reserve force in the rear might easily retake the territory after the fighters have headed for friendly bases and the ships quieted their guns. Bombay is the classic case for this (unless the Japanese are willing to lose an airforce to gain a victory city with a minor complex on it). Such trades will most likely lead to short-term losses for you, but long-term gains.
In the Pac, the Caroline make for an interesting get for naval operations. Iwo Jima or the Soviet Far East is more intriguing for air operations. Iwo Jima, however, is not an edge, nor a nibble. Many like to move to coastal Australia and subsequently take back the money islands. Coordination with the Anzac navy can tip the scale defensively in our favor, particularly when Japan is clawing for the quick capture of the Jewel of the Empire. Planes can be launched like spears from carriers and land in the thick of the Asian campaign. If planned properly, planes leaving can be replaced the same turn with planes arriving.